Question

15) Assume that the height of adult females in the United States is approximately normally distributed with a mean of 64.1 inches and a standard deviation of 2.86 inches. A sample of 8 such women is selected at random. Find the probability that the mean height of the sample is greater than 63.5 inches.

Round your answer to 4 decimal places.

Answer 1

Solution :

Given that ,

mean = = 64.1

standard deviation = = 2.86

n = 8

= 64.1

= / n = 2.86 / 8 = 1.0112

P( > 63.5) = 1 - P( < 63.5)

= 1 - P[( - ) / < (63.5 -64.1) /1.0112 ]

= 1 - P(z <-0.59 )

Using z table

= 1 - 0.2776

= 0.7224

probability= 0.7224