The diameter of a brand of tennis balls is approximately normally distributed, with a mean of 2.71 inches and a standar
Posted: Mon Jul 11, 2022 11:43 am
The diameter of a brand of tennis balls is approximatelynormally distributed, with a mean of 2.71 inches and astandard deviation of 0.05 inch. A random sample of 12 tennis ballsis selected. Complete parts (a) through (d) below.
Question content area bottom
Part 1
a. What is the sampling distribution of the mean?
A.
Because the population diameter of tennis balls is approximatelynormally distributed, the sampling distribution of samples ofsize 12 will also be approximately normal.
B.
Because the population diameter of tennis balls is approximatelynormally distributed, the sampling distribution of samples ofsize 12 cannot be found.
C.
Because the population diameter of tennis balls is approximatelynormally distributed, the sampling distribution of samples ofsize 12 will not be approximately normal.
D.
Because the population diameter of tennis balls is approximatelynormally distributed, the sampling distribution of samples ofsize 12 will be the uniform distribution.
b. What is the probability that the sample mean is less than2.70 inches?
P(X<2.70)=enter your response here
(Round to four decimal places as needed.)
c. What is the probability that the sample mean is between 2.69and 2.73 inches?
P(2.69<X<2.73)=enter your response here
(Round to four decimal places as needed.)
d. The probability is 56% that the sample mean will becentered between what two values, symmetrically distributedaround the population mean (so that 28% of the area isless than the mean and 28% is greater thanthe mean)?
The lower bound is
enter your response here
inches. The upper bound is
enter your response here
inches.
(Round to two decimal places as needed.)
Question content area bottom
Part 1
a. What is the sampling distribution of the mean?
A.
Because the population diameter of tennis balls is approximatelynormally distributed, the sampling distribution of samples ofsize 12 will also be approximately normal.
B.
Because the population diameter of tennis balls is approximatelynormally distributed, the sampling distribution of samples ofsize 12 cannot be found.
C.
Because the population diameter of tennis balls is approximatelynormally distributed, the sampling distribution of samples ofsize 12 will not be approximately normal.
D.
Because the population diameter of tennis balls is approximatelynormally distributed, the sampling distribution of samples ofsize 12 will be the uniform distribution.
b. What is the probability that the sample mean is less than2.70 inches?
P(X<2.70)=enter your response here
(Round to four decimal places as needed.)
c. What is the probability that the sample mean is between 2.69and 2.73 inches?
P(2.69<X<2.73)=enter your response here
(Round to four decimal places as needed.)
d. The probability is 56% that the sample mean will becentered between what two values, symmetrically distributedaround the population mean (so that 28% of the area isless than the mean and 28% is greater thanthe mean)?
The lower bound is
enter your response here
inches. The upper bound is
enter your response here
inches.
(Round to two decimal places as needed.)