Mid-Year Review Questions - AP Statistics
# 1) X~N(30, 10) Y~N(20, 10) Z=X-Y
a) What is the distribution of Z? Z~___________
b) Find P(Z>15)
c) Find P(11 < Z < 16)
# 2) The probability a car is red is 20% for all cars produced for sale in the USA. A simple random sample (SRS) of 64 cars is taken. p-hat is the proportion of cars that are found to be red.
Find:
a) What is the sampling distribution for p-hat?
p-hat~ _____________________
b) P(p-hat>.23) =
c) P(0.195 < p-hat < .215) =
# 3) Referring to the information provided in question 2, an individual decides to randomly collect 10 cars. He collects the cars one by one.
a) Calculate the probability that exactly 1 car is red. Calculate this by hand.
b) Calculate the probability that at least 1 car is red.
c) What is the probability that the first red car he collects is his third car?
d) On average, how many cars can he expect to collect before getting his first red car?
# 4) X~N(20, 15) => A simple random sample of sample size 100 is drawn from this population.
a) What is the sampling distribution for x-bar for your sample?
x-bar~ _______________
b) Calculate P(x-bar <23)
c) Calculate P(X<23)
a) What is the distribution of Z? Z~___________
b) Find P(Z>15)
c) Find P(11 < Z < 16)
# 2) The probability a car is red is 20% for all cars produced for sale in the USA. A simple random sample (SRS) of 64 cars is taken. p-hat is the proportion of cars that are found to be red.
Find:
a) What is the sampling distribution for p-hat?
p-hat~ _____________________
b) P(p-hat>.23) =
c) P(0.195 < p-hat < .215) =
# 3) Referring to the information provided in question 2, an individual decides to randomly collect 10 cars. He collects the cars one by one.
a) Calculate the probability that exactly 1 car is red. Calculate this by hand.
b) Calculate the probability that at least 1 car is red.
c) What is the probability that the first red car he collects is his third car?
d) On average, how many cars can he expect to collect before getting his first red car?
# 4) X~N(20, 15) => A simple random sample of sample size 100 is drawn from this population.
a) What is the sampling distribution for x-bar for your sample?
x-bar~ _______________
b) Calculate P(x-bar <23)
c) Calculate P(X<23)