Question

The diameter of a brand of tennis balls is approximately normally distributed, with a mean of 2.71 inches and a standard deviation of 0.05 inches. A random sample of 11 tennis balls is selected. What is the probability that the sample mean is between 2.70 and 2.72 inches

Answer 1

SOLUTION:

From given data,

The diameter of a brand of tennis balls is approximately normally distributed, with a mean of 2.71 inches and a standard deviation of 0.05 inches. A random sample of 11 tennis balls is selected. What is the probability that the sample mean is between 2.70 and 2.72 inches.

Mean = = 2.71

Standard deviation = = 0.05

Sample size = n = 11

Then,

= = 2.71

= / sqrt(n) = 0.05 / sqrt(11) = 0.01507

Z = ( - ) / = ( - 2.71) / 0.01507

Now,

The probability that the sample mean is between 2.70 and 2.72 inches.

P (2.70 < < 2.72) = P ((2.70 - 2.71) / 0.01507​​​​​​​ < ( - ) /   < (2.72 - 2.71) / 0.01507​​​​​​​)

P (2.70 < < 2.72) = P (-0.01/ 0.01507​​​​​​​ < Z < 0.01 / 0.01507​​​​​​​)

P (2.70 < < 2.72) = P (-0.66​​​​​​​ < Z < 0.66​​​​​​​)

P (2.70 < < 2.72) = P (Z < 0.66​​​​​​​) - P (Z < - 0.66 )

P (2.70 < < 2.72) = 0.74537 - 0.25463

P (2.70 < < 2.72) = 0.49074

The probability that the sample mean is between 2.70 and 2.72 inches is 0.49074.

Please thumbs-up / vote up this answer if it was helpful. In case of any problem, please comment below. I will surely help. Down-votes are permanent and not notified to us, so we can't help in that case.