Question

A distribution of values is normal with a mean of 46.9 and a standard deviation of 32.2. Find the probability that a randomly selected value is between 8.3 and 50.1. P(8.3 < X < 50.1) =

Answer 1

Solution :

Let X represents the distribution of values that is normally distributed.

Given that, X ~ N(46.9, 32.2²)

μ = 46.9 and  σ = 32.2

a) We have to find P(8.3 < X < 50.1).

P(8.3 < X < 50.1) = P(X < 50.1) - P(X ≤ 8.3)

We know that, if X ~ N(μ, σ²) then,

Using "pnorm" function of R we get,

P(Z < 0.0994) = 0.5396 and P(Z ≤ -1.1988) = 0.1153

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