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MATH 110 MODULE 5 QUIZ: Problem Set (ACTUAL NEW
VERSION UPDATE QUIESTIONS AND ANSWERS 2025-2026)
Portage Learning
Suppose that you are attempting to estimate the weight of 600 parts. In order to use the infinite standard deviation formula, what sample size, n, should you use? Your Answer: n/N0. n/6000. 600 * 0.05= Sample should be less than or equal to 30 In order to use infinite standard deviation formula, we must have: So, the sample size must be less than 30. Suppose that you take a sample of size 15 from a population that is known to be normally distributed. Can the sampling distribution of x̄> be approximated by a normal probability distribution? Your Answer: YES, because the population is known to be normally distributed.
Question 1
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Question 2
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Yes, the sampling distribution of x̄> can be approximated by a normal probability distribution because the population is normally distributed. (Recall that if the population is normally distributed, the sampling distribution of x̄> can be approximated by a normal probability distribution even for very small sample sizes.) Question 3
within $400 of the population mean μ of $52,400.) Calculate the z-score:
Using this formula, we will calculate the two z-scores that we will use to answer our question. We will round these values to -.81 and .81, respectively. So, we want to find P(-.81< Z < .81) on the standard normal probability distribution table. Recall that P(-.81< Z < .81)=P(Z<.81)-P(Z<-.81)=.79103 -.20897 = .58206. So now we know that there is a 0.58206 probability that a simple random sample of 50 members of the sales force will provide a sample mean that is within the $400 of the sample mean. Conversely, there is a 1 - .58206= .41794 probability the sample mean will not be within the $400 range. Suppose that you have a large number of potatoes. The mean weight of the potatoes is 7.4 ounces with a standard deviation of 2.2 ounces. We may assume a normal distribution. a) If you choose 25 potatoes at random, what is the probability that the mean of this sample of 25 potatoes is between 7 and 8 ounces?
Question 5
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Your Answer: a. sample SD =2.2/ square root of 25=0.44 z score for 7 ounces = 7- 7.4/0.44=-0. z score for 8 ounces = 8-7.4/0.44=1. P(-0.91 Z 1.36) =.91309-.18141=0. b. sample SD =2.2/ square root of 45=0.328 z score for 7 ounces = 7- 7.4/0.328=-1. P( Z -1.22)=. c. sample SD =2.2/ square root of 40=0.348 z score for 7.5 ounces = 7.5- 7.4/0.348=0.287 P greater than 0.287=. so 1-.61409=0. a) We calculate the standard deviation of the sample distribution: Calculate the z-score for 7 ounces:
Calculate the z-score for 8 ounces: So, we want to find P(-.91< Z < 1.36) on the standard normal probability distribution table. Recall that P(-.91< Z < 1.36)=P(Z<1.36)-P(Z<-.91)=.91309-.18141=.73168.
P(Z > .29) = 1 - P(Z < .29) = 1-.61409=.38591.
Therefore, there is a .38591 probability that a simple random sample of 40 potatoes will have a mean weight greater than 7.5 ounces.
Question 6
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According to the American Diabetes Association (2013), 8.3 % of the U.S. population have diabetes. a) Suppose that you take a random of 80 Americans, what is the probability that 7 % or less of these 80 people have diabetes? b) Suppose that you take a random of 120 Americans, what is the probability that 8 % or more of these 120 people have diabetes? Your Answer: a. 80 Americans with 7% or less p=0.083 n= SD population = square root of. (1-.083)/80=0.3084 z=0.07-0.083/0.3084=-0. =. b. 120 Americans with 8% or more p=0.083 n= SD population = square root of. (1-.083)/120=0.0252 z=0.08-0.083/0.0252=-0. 1-.45224=. a) Now we use our old friend the z-score to determine the probability of our sample
We want P(Z<-0.42). From the standard normal table, we find: P(Z<-0.42)=.33724. So there is a .33724 probability that the percentage of the sample that has diabetes is less than 7 %. b) Now we use our old friend the z-score to determine the probability of our sample size yielding a proportional mean p within the desired range: We want P(Z>-0.12). From the standard normal table, we find: P(Z>-.12)=1- P(Z<-.12)=1-.45224=.54776. So there is a .54776.probability that the percentage of the sample that has diabetes is greater than 8 %. As a reminder, the questions in this review quiz are a requirement of the course and the best way to prepare for the module exam. Did you complete all questions in their entirety and show your work? Your
Question 7
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Answer: YES
