The diameter of a brand of tennis balls is approximately normally distributed, w

Question

The diameter of a brand of tennis balls is approximately normally distributed, with a mean of 2.62 inches and a standard deviation of 0.05 inch. A random sample of 10 tennis balls is selected. Complete parts (a) through (d) below. a. What is the sampling distribution of the mean? OA. Because the population diameter of tennis balls is approximately normally distributed, the sampling distribution of samples of size 10 will not be approximately O B. Because the population diameter of tennis balls is approximately normally distributed, the sampling distribution of samples of size 10 will be the uniform 0 C Because the population diameter of tennis balls is approximately normally distributed the sampling distribution of samples of size 10 cannot be found. normal. distribution. D.Because the population diameter of tennis balls is approximately normally distributed, the sampling distribution of samples of size 10 will also be approximately normal. b. What is the probability that the sample mean is less than 2.59 inches? P(X

Explanation / Answer

1) here std error of mean =std deviaiton/(n)1/2 =0.05/(10)1/2 =0.0158

therefore P(X<2.59)=P(Z<(2.59-2.62)/0.0158)=P(Z<-1.8974)=0.0289

2)

a) std error of mean =std deviaiton/(n)1/2 =3/(25)1/2 =0.6

therefore P(22.5<X<23.5)=P(-0.8333<Z<0.8333)=0.7977-0.2023 =0.5953

3)

a)

std error of mean =std deviaiton/(n)1/2 =5/(25)1/2 =1

therefore P(X>23)=P(Z>2)=0.0228

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