Question

Given that x is a normally distributed random variable with a mean of 50 and a standard deviation of 2, find the probability that x is between 46and 54.

Answer 1

P = 0.9544

Explanation:

Firs,t we need to standardize 46 and 54 using the following equation:

`z=(x-m)/(s)`

Where m is the mean and s is the standard deviation for the random variable.

Replacing m by 50 and s by 2, we find that 46 and 54 are equivalent to:

`z=(46-50)/(2)=-2\\z=(54-50)/(2)=2`

Then, the probability that x is between 46 and 54 is equal to:

P(46<x<54) = P(-2<z<2)

So, using the normal table, we can find the probability as:

P(-2<z<2) = P(z<2) - P(z<-2)

P(-2<z<2) = 0.9772 - 0.0228

P(-2<z<2) = 0.9544