Download T F 1) The following distribution is a probability distribution function

T F 1) The following distribution is a probability distribution function. x -1 0 1 2 3 p(x) .4 .25 .05 .2 .1
Answer: True
T F 2) The area under a normal curve between z = -2.15 and z = 0 is -0.4842.
Answer: False
T F 3) -1 <P(X=i)<= 1 ---- I guess is what you meant! The <, = signs are missing!
Answer: if this is what was meant the statement is True. If not please relist this problem
T F 4) Trials in a binomial experiment must be independent and identical.
Answer: True
T F 5) A professor wants to find out the top 2.5% grades of his class, then the z-score used to calculate
the cut-off point would be 1.96.
Answer: True
T F 6) If a sample n=25 is selected from a binomial population with p=0.86, then the normal
approximation to binomial could be used to compute the probability.
Answer: True
T F 7) Mean, mode, and median of a normal distribution are located at the center.
Answer: True
T F 8) The range of a 95% C.I. is wider than the range of a 90% C.I.
Answer: True
T F 9) Two numbers used to describe a normal curve (distribution) are the mean and standard deviation.
Answer: True
T F 10) The director of a marketing company believes that the probability of making a sale when a call is
made to individual’s home is 0.05. The probability of making less than two sales in a sample of twenty
calls is 0.735.
Answer: True
T F 11) The standard normal distribution is a normal distribution with a mean of 1 and standard
deviation of 0.
Answer: False
T F 12) The Central Limit Theorem states that the sample mean will be the same as the population mean
if the sample size is large.
Answer: True
Problems
You must write your answers on the provided answer sheet. Note: All problems relate to probability, the
answer must have 4 decimal points for the normal distribution and 3 decimal points for binomial
distribution.
1) A raffle offers a first prize of $500, and two second prizes of $50 each. One ticket costs $2, and
1000 tickets are sold. Find the expected winnings for a person who buys one ticket.
Answer: expected winnings -$1.40 ( or restated, an expected loss of $1.40)
2) A political candidate estimates that 30% of the votes in his party favor his proposed tax reform
bill. If there are 400 people at a rally, find the probability that at least 130 favor his tax bill.
Answer : 0.151
3) A farmer wants to try a new experimental diet on his hogs. He wants to be 99% confident that
the average weight gain will be within 2 pounds. If the standard deviation is 16.5 pounds, how
many hogs should receive the new experimental diet?
Answer: 452 hogs
4)
A book store owner decides to sell children’s talking books that will appeal to the middle 34% of
his customers. The owner studies that mean price of children’s talking books is $34.80 with a
standard deviation of $9.50. Find the minimum price of talking books the owner should sell.
Assume the variable is normally distributed.
Answer: $30.62
5) For a binomial random variable with n=12 and p=.4, compute the following.
a) P(X <=4) b) P(3<= X<=10) ------- Again I am making an educated guess. If that is what you
meant the answers are below. If not please repost this problem.
Answers: a) 0.4382 b) 0.91624
6) a) Compute P(-1.52<= z <=-0.25)
THIS WAS CORRECT!
b) Find the value of z such that P(Z<=z)=.2090
Answers: a) 0.337 b) z= - 0.81
7) Suppose the probability to have a boy or girl is equal, what is the probability that a random selected
family of five children will have at least one boy? Hint: probability to have a boy is 0.5.
Answer: probability of at least one boy is 31/32 = 0.96875
8) Ten randomly selected shut-ins were each asked to list how many hours of television they watched
per week. The results were: 82 66 90 84 75 88 80 94 110 91. Compute 98% confidence interval for the
mean number of hours of television watched per week by the shut-ins.
Answer: 98% confidence interval [ 77.29, 94.71]