Question

A random variable is normally distributed with a mean of μ = 50 and a standard deviation of σ = 5. What is the probability that the random variable will assume a value that is less than 40? Make sure your answer is between 0 and 1, round to four digits.

Answer 1

Answer

we have mean = 50 and standard deviation = 5

we have to find the probability that a value is less than 40

Using the formula

setting

we get

it gives us,

Using the identity

we can write it as (using z distribution table)

So, the required probability that a value will be less than 40 is 0.0228 (rounded to 4 decimal places)