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 2.77 inches and a standard deviaton of 0.04 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? O A Because the population diameter o tennis balls is approximately normally distributed the sampling dsnbution o samples o size 0 will be the uniform distribution. O B. Because the population diameter of tennis balls is approximately normally distributed, the sampling distribution of samples of size 10 will not be approximately normal. C. Because the population diameter o tennis balls is approximately normally distributed the sampling distribution o samples o size 0 cannot be un D Because he population dia meter o ennis balls is approximately normally distribu e the sampling disr bution of samples of size 10 w a so be approximate normal b. What is the probability that the sample mean is less than 2.74 inches? P(X2.74)- Round to four decimal places as needed.) c. What is the probability that the sample mean is between 2.75 and 2.79 inches? P(2.75c X

Explanation / Answer

a) D - Sampling distribution will be approximately normal

b) Z=(2.74-2.77)/0.04=-0.75

P(z<-0.75)=0.226627

c) Z= (2.75-2.77)/0.04=-0.5 and +0.5

P(-0.5<z<0.5)=0.3829

d) 58 % means z value is 29% above mean.

Z = 0.806421 and -0.806421

Lower bound=2.77-0.806421*0.04=2.7377

Upper bound =2.77+0.806421*0.04=2.8022

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