Question

The diameter of a brand of tennis balls is approximately normally​ distributed, with a mean of 2.52

inches and a standard deviation of 0.04 inch. A random sample of 11 tennis balls is selected .

a. what is probability that sample mean is between 2.50 and 2.54 inches?

Part 2

given a normal distributuon with m =104 and s= 10 and given you select a sample of n=4

2a. there is a 62% chance x bar is above what value?

Answer 1

Solution :

a ) Given that,

mean = = 2.52

standard deviation = = 0.04

n = 11

= 1200

= / n = 0.04 11 = 0.0121

P ( 2.50 < < 2.54 )

P ( 2.50 - 2.52 / 0.0121 ) < ( -  / ) < ( 2.54 - 2.52 / 0.0121 )

P ( - 0.02 / 0.0121 < z < 0.02 / 0.0121 )

P (-1.65 < z < 1.65 )

P ( z < 1.65 ) - P ( z < -1.65)

Using z table

= 0.9505 - 0.0495

= 0.9010

Probability = 0.9010

b ) Given that,

mean = M =104

standard deviation = S = 10

Using standard normal table,

n = 4

M = 104

S = / n = 10 4 = 5

P( Z > z) = 62%

P(Z > z) = 0.62

1 - P( Z < z) = 0.62

P(Z < z) = 1 - 0.62

P(Z < z) = 0.38

z = -0.30

Using z-score formula,

= z * S + M

= -0.30 * 5 + 70

= 8.5