Answer:
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