A normal population has mean = μ9 and standard deviation = σ5. (a) What proportion of the population is less than 20? (b) What is the probability that a randomly chosen value will be greater than 6? Round the answers to four decimal places.

Step-by-step explanation:

We would apply the formula for normal distribution which is expressed as

z = (x - µ) / σ

Where

x = randomly chosen values.

µ = mean

σ = standard deviation

From the information given,

µ = 9

σ = 5

1) The proportion of the population that is less than 20 is expressed as

P (x < 20)

For x = 20

z = (20 - 9) / 5 = 2.2

Looking at the normal distribution table, the probability corresponding to the z score is 0.986

P (x < 20) = 0.986

2) The probability that a randomly chosen value will be greater than 6 is expressed as

P (x > 6) = 1 - P (x ≤ 6)

For x = 6

z = (6 - 9) / 5 = - 0.6

Looking at the normal distribution table, the probability corresponding to the z score is 0.27

P (x > 6) = 1 - 0.27 = 0.73