Question

A normal population has mean

=μ63 and standard deviation =σ16

(a) What proportion of the population is greater than

100

(b) What is the probability that a randomly chosen value will be less than

80

Answer 1

Solution :

We have, X ~ N(63, 16²)

μ = 63 and  σ = 16

a) We have to find P(X > 100).

We know that if X ~ N(μ, σ²) then,

Using "pnorm" function of R we get, P(Z > 2.3125) = 0.0104

Hence, the proportion of population that is greater than 100 is 0.0104.

b) We have to find P(X < 80).

We know that if X ~ N(μ, σ²) then,

Using "pnorm" function of R we get, P(Z < 1.0625) = 0.8560

Hence, the probability that a randomly chosen value will be less than 80 is 0.8560.

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