Question

The height of plants is normally distributed with a mean of 32 inches and a standard deviation of 8 inches. What is the probability that the average height of a sample of 25 plants is greater than 30 inches

Answer 1

Solution :

Given that,

mean = = 32

standard deviation = = 8

n = 25

=   = 32

= / n = 8 / 25 = 1.6

P( > 30) = 1 - P( < 30)

= 1 - P[( - ) / < (30 - 32) / 1.6]

= 1 - P(z < -1.25)

Using z table,    

= 1 - 0.1056

= 0.8944