SECTION 11.4 HOMEWORK
Directions: Use the normal approximation to the binomial random variable to solve problems 1-5.
1) Let X be a binomial random variable with n = 1650 and p = 0.55. Find:
a) P (X ≥ 928) b) P(X ≤ 882) c) P(890 ≤ X ≤ 938) d) P(X ≤ 879 or X ≥ 947)
2) A coin is weighted so that the probability of getting a head when the coin is flipped is 2/3. If the coin
is flipped 250 times, find the probability of
a) obtaining at most 157 heads.
b) obtaining at least 170 heads.
c) obtaining between 160 and 165 heads, inclusive.
d) obtaining 225 or more heads.
3) Suppose that 15% of all items produced by an assembly line are defective. If 700 items are selected at
random from this assembly line, find the probability that
a) 84 or fewer items are defective.
b) between 100 and 110 items, inclusive, are defective.
c) 125 or more items are defective.
4) Suppose that 60% of the people in a large city oppose an increase in the property tax. If 2500 people
are selected at random, what is the probability that 950 or more of them will favor an increase in the
property tax?
5) It is estimated that 30% of all cars in a particular city would fail an exhaust emissions test. If 250 cars
are randomly selected for testing, what is the probability that 170 or more will pass the test?
Directions: For problems involving a binomial experiment,
if n < 10 use the formula for binomial probabilities.
If it is binomial and n ≥ 10, then
either A) use the normal approximation if it is valid
or B) if the normal approximation is not valid, write "NOT VALID", do not solve the
problem, and go on to the next problem.
6) A new drug used to combat PMS is effective 88% of the time. If, 5 women use this drug, find the
probability that exactly 3 found the drug to be effective.
7) Juan's instructor gave a 10-question multiple-choice test. Juan is totally unprepared and decides to
guess on each question. Each question has a choice of 5 answers. What is the probability that' Juan will
answer at least 8 questions correctly?
8). The residents of a certain Eastern suburb average 42 minutes a day commuting to work, with a
standard deviation of 12 minutes. Assuming that commuting times are normally distributed, find the
probability that a resident of this community commutes no more than 35 minutes a day.
9) An unbiased die is rolled 300 times. What is the probability that a two shows on the upturned face at
least 60 times?
10) The life of a certain type of light bulb is normally distributed with mean 500 hours and standard
deviation 100 hours. What percentage of the bulbs can be expected to last between 650 and 780 hours?
11) From records of past performances, the probability that a student passes Professor Smith's statistics
course is 0.45. Four students are selected at random from Professor Smith's class. Find the probability
that all four pass the course.
Answers: 1a) .1611 1b) .1075 1c) .7503 1d) .1091
2a) .1093 2b) .3520 2c) .2679 2d) ≈ 0 3a) .0150
3b) .4380 3c) .019 4) .9803 5) .7764 6) .0981
7) NOT VALID 8) .2810 9) .0708 10) .0642 11) .0410