1) Let x be a random variable representing the cost a childcare center charges for one child for a day. Consider a sampling distribution of sample means,(x.
a) As the sample size becomes increasingly large, what does the distribution of sample means approach?
b) What value will the mean ((x approach?
c) What value will the standard deviation ((x approach?
d) How do the (x distribution for samples of size n = 40 and n = 80 compare?
2) The number of boxes of girl scout cookies sold by each of the girl scouts in a Midwestern city has a distribution which is approximately normal with mean ( = 75 boxes and standard deviation ( = 30 boxes.
a) Find the probability that a scout chosen at random sold between 60 and 90 boxes of cookies.
b) Find the probability that the sample mean number of boxes of cookies sold by a random sample of 36 scouts is between 60 and 90 boxes?
3) Statistical Abstracts (117th edition) reports sale price of unleaded gasoline (in cents per gallon) at the refinery. The distribution is mound-shaped with mean ( = 80.04 cents per gallon and standard deviation, ( = 4.74 cents per gallon.
a) Are we likely to get good results if we use the normal distribution to approximate the distribution of sample means for samples of size 9? Explain.
b) Find the probability that for a random sample of size 9, the sample mean price will be between 79 and 82 cents per gallon.
c) Find the probability that for a random sample of size 36, the sample mean price will be between 79 and 82 cents per gallon.
d) Compare your answers for parts (b) and (c) and give a reason for the difference.
4) More than 200 billion grocery coupons are distributed each year for discounts exceeding $84 billion. However, according to a report in USA Today, only 3.2% of the coupons are redeemed. If a company distributes 5000 coupons, what is the probability that:
a) at least 100 coupons are redeemed?
b) at most 200 coupons are redeemed?
c) fewer than 100 coupons are not redeemed?
d) more than 200 coupons are not redeemed?
a) As the sample size becomes increasingly large, what does the distribution of sample means approach?
b) What value will the mean ((x approach?
c) What value will the standard deviation ((x approach?
d) How do the (x distribution for samples of size n = 40 and n = 80 compare?
2) The number of boxes of girl scout cookies sold by each of the girl scouts in a Midwestern city has a distribution which is approximately normal with mean ( = 75 boxes and standard deviation ( = 30 boxes.
a) Find the probability that a scout chosen at random sold between 60 and 90 boxes of cookies.
b) Find the probability that the sample mean number of boxes of cookies sold by a random sample of 36 scouts is between 60 and 90 boxes?
3) Statistical Abstracts (117th edition) reports sale price of unleaded gasoline (in cents per gallon) at the refinery. The distribution is mound-shaped with mean ( = 80.04 cents per gallon and standard deviation, ( = 4.74 cents per gallon.
a) Are we likely to get good results if we use the normal distribution to approximate the distribution of sample means for samples of size 9? Explain.
b) Find the probability that for a random sample of size 9, the sample mean price will be between 79 and 82 cents per gallon.
c) Find the probability that for a random sample of size 36, the sample mean price will be between 79 and 82 cents per gallon.
d) Compare your answers for parts (b) and (c) and give a reason for the difference.
4) More than 200 billion grocery coupons are distributed each year for discounts exceeding $84 billion. However, according to a report in USA Today, only 3.2% of the coupons are redeemed. If a company distributes 5000 coupons, what is the probability that:
a) at least 100 coupons are redeemed?
b) at most 200 coupons are redeemed?
c) fewer than 100 coupons are not redeemed?
d) more than 200 coupons are not redeemed?
