The heights of a certain population of corn plants follow a

The heights of a certain population of corn plants follow a normal distribution with mean 145 cm and a standard deviation 22 cm. Define Y as the heigth in cm of a randomly selected corn plant.

What is the height of a corn plant that is said to to be at the 13th percentile in height?

P(Y< __ ) = P( Z < ___ ) = _____

What is the height of a corn plant that is said to to be at the upper 4th percentile in height?

P(Y > __ ) = P( Z >___ ) = _____

Find the probability that none of the four plants will be more than 150 cm tall. Answer with 4th decimal accuracy.

P(X=0) =

Solution

mean = 145

sd = 22

P(Y < y1) = 0.13

=> P(Z < (y1 - 145)/22) = 0.13

From the standard normal table, for the corresponding probability of 0.13 Z value = -1.126

=> (y1 - 145)/22) = -1.126

=> y1 = 120.228

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P(Y > y2) = 0.04

=> P(Z > (y2 - 145)/22) = 0.04

From the standard normal table, for the corresponding probability of 0.04 Z value = 1.751

=> (y2 - 145)/22) = 1.751

=> y2 = 183.522

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P( Y < 150) = P(Z < (150-145)/22)

= P(Z < 0.227)

= 0.5898

probability that none of the four plants will be more than 150 cm tall = 0.5898*0.5898*0.5898*0.5898

= 0.1210