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The Normal Distribution - Statistical Techniques | SPEA, Exams of Environmental Science

Indiana University Bloomington (IU)Environmental Science
Prof. Henry Wakhungu

Material Type: Exam; Professor: Wakhungu; Class: STATISTICAL TECHNIQUES; Subject: Public And Environmental Affairs; University: Indiana University - Bloomington; Term: Fall 2009;

Typology: Exams

Pre 2010

Uploaded on 12/06/2009

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Chapter 6 - The Normal Distribution
1. When the data values are evenly distributed about the mean, the distribution is said to be
__________.
Ans: symmetrical
2. Give the type of distribution pattern that occurs when the majority of the data values fall
to the left of the mean?
A) symmetrical B) positively skewed C) negatively skewed D) left skewed
Ans: B
3. When the majority of the data values fall to the right of the mean, the distribution is said
to be left skewed.
Ans: True
4. The figure below is an example of a negatively skewed distribution.
Ans: False
5. A(n) __________ is another term which can be used to describe an approximately bell
shaped curve.
Ans: approximately normally distributed
6. On an easy test, the mean score was 97 out of a possible 100 points. The distribution of
all test scores is mostly lilkely to be
A) symmetric C) positively skewed
B) negatively skewed D) diagonally skewed
Ans: B
7. Which of the following properties does not apply to a theoretical normal distribution?
A) The normal distribution is bell-shaped.
B) The mean, median, and mode are equal.
C) The normal distribution is bimodal.
D) The curve never touches the x-axis.
Ans: C
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  1. When the data values are evenly distributed about the mean, the distribution is said to be __________. Ans: symmetrical
  2. Give the type of distribution pattern that occurs when the majority of the data values fall to the left of the mean? A) symmetrical B) positively skewed C) negatively skewed D) left skewed Ans: B
  3. When the majority of the data values fall to the right of the mean, the distribution is said to be left skewed. Ans: True
  4. The figure below is an example of a negatively skewed distribution. Ans: False
  5. A(n) __________ is another term which can be used to describe an approximately bell shaped curve. Ans: approximately normally distributed
  6. On an easy test, the mean score was 97 out of a possible 100 points. The distribution of all test scores is mostly lilkely to be A) symmetric C) positively skewed B) negatively skewed D) diagonally skewed Ans: B
  7. Which of the following properties does not apply to a theoretical normal distribution? A) The normal distribution is bell-shaped. B) The mean, median, and mode are equal. C) The normal distribution is bimodal. D) The curve never touches the x -axis. Ans: C
  1. In applied statistics, the area under the normal distribution curve is more important than the frequencies. Ans: True
  2. The normal distribution curve can be used as a probability distribution curve for normally distributed variables. Ans: True
  3. The total area under the normal distribution curve is approximately 0.99 but can never be equal to 1.0. Ans: False
  4. If a normal distribution has mean 16 and standard deviation 3, then A) the median is 16 C) the median is 19 B) the median is 13 D) the medians are 13 and 19 Ans: A
  5. For a normal curve with mean 8 and standard deviation 7, which of the following parts of the normal curve will have an area of approximately 68%? A) from 4.5 to 11.5 B) from 1 to 15 C) from 8 to 22 D) from –6 to 22 Ans: B
  6. The area under the normal distribution curve that lies within three standard deviations of the mean is approximately 95%. Ans: False
  7. One normal curve has mean 23 and standard deviation 1, a second normal curve has mean 5 and standard deviation 10. The curve that is more dispersed, or spread out, is A) The first normal curve B) The second normal curve C) They are equally spread out D) There is insufficient information to answer the question Ans: B
  8. For a normal curve with mean 6 and standard deviation 4, which of the following parts of the normal curve will have an area of approximately 34%? A) from 4 to 10 B) from 2 to 10 C) from 6 to 10 D) from –2 to 14 Ans: C
  9. What is the special property of the standard normal distribution, compared to other normal distributions? A) The mean is 0 and the standard deviation is 1. B) The total area under the normal distribution curve is equal to 1.00. C) The curve is continuous. D) The mean is located at the center of the distribution.
  1. The z value corresponding to 48.81% of the data is 2.20 in Table E of Appendix C. Ans: False

22. The P^ a^0 ^ z ^2.^25 f^ is 0.4878.

Ans: True

  1. Find the probability P(Z < 0.17) using the standard normal distribution. A) 0.8300 B) 0.4325 C) 0.5675 D) 0. Ans: C
  2. Find the probability P(z < –0.41) using the standard normal distribution. A) 0.6591 B) 0.3409 C) 0.8409 D) 0. Ans: C
  3. Find the probability P(z > 0.78) using the standard normal distribution. A) 0.2200 B) 0.7823 C) 0.7177 D) 0. Ans: D
  4. Find the probability P(z > –0.64) using the standard normal distribution. A) 0.2611 B) 0.7389 C) 0.7611 D) 0. Ans: A
  5. In the figure below, what is the area under the curve between z^ ^1.^50 and z^ ^2.^50? A) 0.0802 B) 0.0606 C) 0.0764 D) 1. Ans: B
  6. Find the area under the curve between z^ ^2.^05 and z^ ^2.^05. A) 0.4938 B) 0.4798 C) 0.9596 D) 0. Ans: C
  1. Find the area under the curve to the left of z^ ^1.^69. A) 0.4545 B) 0.4452 C) 0.9545 D) 0. Ans: C
  2. (^) Find the probability for P^ (^0 ^ z ^1.^67 ). A) 0.4525 or 45.25% C) 0.4207 or 42.07% B) 0.4554 or 45.54% D) 0.3554 or 35.54% Ans: A
  3. The area under the curve is always positive even if the z value is negative. Ans: True
  4. The area to the right of z^ ^1.^83 is 0.4256. Ans: False
  5. Stating that the area under the curve between z^ ^0 and z^ ^1.^00 is 0.3413 is the same as stating that the __________ of selecting any z value between 0 and 1.00 is 0.3413. Ans: probability
  6. Find the probability P(0.26 < z < 1.33) using the standard normal distribution. A) 0.3057 B) 0.6943 C) 0.8057 D) 0. Ans: A
  7. Find the probability P(–0.77 < z < –0.16) using the standard normal distribution. A) 0.0400 B) 0.7842 C) 0.3458 D) 0. Ans: D
  8. Find the probability P(–1.14 < z < 1.01) using the standard normal distribution. A) 0.8400 B) 0.2834 C) 0.7166 D) 0. Ans: C
  9. For a normal distribution with mean 5 and standard deviation 6, the value 11 has a z value of A) –1 B) 1 C) 2 D) 3 Ans: B
  1. What z value corresponds to 17% of the data between the mean and the z value? A) 1.25 B) 0.44 C) 0.52 D) 2. Ans: B
  2. The z value that corresponds to the 40th percentile is z^ ^1.^72. Ans: False
  3. What is the z value to the right of the mean such that 85% of the total area lies to the left of it as shown in the figure below? Ans: 1.
  4. In order to be accepted into a top university, applicants must score within the top 5% on the SAT exam. Given that the test has a mean of 1000 and a standard deviation of 200, what is the lowest possible score a student needs to qualify for acceptance into the university? A) 1330 B) 1400 C) 1250 D) 1100 Ans: A
  5. Mrs. Smith's reading class can read a mean of 175 words per minute with a standard deviation of 20 words per minute. The top 3% of the class is to receive a special award. What is the minimum number of words per minute a student would have to read in order to get the award? Ans: 213
  6. If X is a normal random variable with mean 8, and if the probability that X is less than 8.88 is .72 (as shown below), then what is the standard deviation of X? (Note: the diagram is not necessarily to scale.) A) 1.00 B) 2.00 C) 2.40 D) 4. Ans: B
  1. If X is a normal random variable with mean 7 and standard deviation 3.0, then find the value x such that P(X< x) is equal to .86, as shown below. (Note: the diagram is not necessarily to scale.) A) 8.32 B) 7.88 C) 7.66 D) 7. Ans: A
  2. If X is a normal random variable with standard deviation 2.50, and if the probability that X is less than 9.45 is .648 (as shown below), then what is the mean of X? (Note: the diagram is not necessarily to scale.) A) 7.6 B) 8.0 C) 8.2 D) 8. Ans: D
  3. If X is a normal random variable with mean 5, and if the probability that X is more than 4.42 is .5910 (as shown below), then what is the standard deviation of X? (Note: the diagram is not necessarily to scale.) A) 2.50 B) 1.67 C) 1.25 D) 0. Ans: A
  1. The standard deviation of sample means will be larger than the standard deviation of the population, and it will be equal to the population standard deviation multiplied by the square root of the sample size. Ans: False
  2. The __________ correction factor is necessary if relatively large samples are taken from a small population, because the sample mean will then more accurately estimate the population mean and there will be less error in the estimation. Ans: finite population
  3. As the sample size n increases, the shape of the distribution of the sample means taken with replacement from a population with mean  and standard deviation of  will approach a normal distribution. This distribution will have a mean of  and a standard deviation of  n (^). This statement summarizes the __________. Ans: central limit theorem
  4. The standard deviation of a distribution is 20. If a sample of 225 is selected, what is the standard error of the mean? Ans: 1.
  5. The average age of doctors in a certain hospital is 45.0 years old with a standard deviation of 6.0 years. If 16 doctors are chosen at random for a committee, find the probability that the mean age of those doctors is less than 45.45 years. Assume that the variable is normally distributed. A) 0.3821 B) 0.4979 C) 0.5939 D) 0. Ans: D
  6. The mean weight of loads of rock is 43.0 tons with a standard deviation of 8.0 tons. If 9 loads are chosen at random for a weight check, find the probability that the mean weight of those loads is less than 40.60 tons. Assume that the variable is normally distributed. A) 0.1841 B) 0.3441 C) 0.2161 D) 0. Ans: A
  7. The average number of mosquitos in a stagnant pond is 70 per square meter with a standard deviation of 8. If 25 square meters are chosen at random for a mosquito count, find the probability that the average of those counts is more than 71.3 mosquitos per square meter. Assume that the variable is normally distributed. A) 0.4119var://n/ B) 0.2119 C) 0.1799 D) 0. Ans: B
  1. The average diameter of sand dollars on a certain island is 5.00 centimeters with a standard deviation of 0.90 centimeters. If 36 sand dollars are chosen at random for a collection, find the probability that the average diameter of those sand dollars is more than 4.820 centimeters. Assume that the variable is normally distributed. A) 0.8592 B) 0.8669 C) 0.8849 D) 0. Ans: C
  2. A survey of 250 lobster fishermen found that they catch an average of 32 pounds of lobster per day with a standard deviation of four pounds. If a random sample of 30 lobster fishermen is selected, what is the probability that their average catch is less than 31.5 pounds? Ans: 24.83%
  3. A television station estimates that 60% of college students watch the Super Bowl. For a sample of 240 students selected at random, what is the mean and variance of the number of students who watch this game? A) Mean = 144.0, Variance = 7.59 C) Mean = 57.6, Variance = 57. B) Mean = 57.6, Variance = 7.59 D) Mean = 144.0, Variance = 57. Ans: D
  4. A(n) __________ is employed when a continuous distribution is used to approximate a discrete distribution. Ans: correction for continuity
  5. A biologist estimates that 60% of deer in the region carry a certain type of tick. For a sample of 300 deer selectetd at random, what is the chance that 186 or fewer deer have this tick? A) 0.8135 B) 0.7782 C) 0.7344 D) 0. Ans: B
  6. A magazine reported that 6% of American drivers read the newspaper while driving. If 500 drivers are selected at random, find the probability that exactly 40 will admit to reading the newspaper while driving. A) 1.96% B) 2.04% C) 1.28% D) 0.56% Ans: C
  7. Of the members of a Boy Scout troop, 15% have received their first aid badge. If 40 boy scouts are selected at random, find the probability that four or more will have the first aid badge? A) 86.65% B) 85.35% C) 36.65% D) 35.35% Ans: A