Question

Suppose x is a normally distributed random variable with μ=30 and σ=5. Find a value  of the random variable x. (Round to two decimal places as needed.)

p(x >): 0.95

Answer 1

Solution :

We have a random variable X which is normally distributed.

μ = 30 and σ = 5

We have to find the value of the random variable X such that P(X > ) = 0.95.

Let the value of the random variable X is k.

Hence, P(X > k) = 0.95

We know that, if X ~ N(μ, σ²) then,

..................(1)

Using "qnorm" function of R we get, P(Z > -1.6448) = 0.95

Comparing, P(Z > -1.6448) = 0.95 and (1) we get,

Hence, the value of the random variable X is 21.78.

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