Question

What percentage of the data in a standard normal distribution lies between x = .09 and x = 1.2?

Answer 1

34.9% of the data in a standard normal distribution lies between x = .09 and x = 1.2.

Explanation:

We have to find the percentage of the data in a standard normal distribution that lies between X = 0.09 and X = 1.2.

As we know that the mean and the standard deviation of a standard normal distribution is 0 and 1 respectively.

The z-score probability distribution for the standard normal distribution is given by;

Z =
`(X-\mu)/(\sigma)` =
`(X-0)/(1)` ~ Standard normal

Now, the percentage of the data in a standard normal distribution that lies between X = 0.09 and X = 1.2 is given by = P(0.09 < X < 1.2)

P(0.09 < X < 1.2) = P(X < 1.2) - P(X
`\leq` 0.09)

P(X < 1.2) = P(
`(X-0)/(1)` <
`(1.2-0)/(1)` ) = P(Z < 1.2) = 0.8849

P(X
`\leq` 0.09) = P(
`(X-0)/(1)`
`\leq`
`(0.09-0)/(1)` ) = P(Z
`\leq` 0.09) = 0.5359

The above probabilities are calculated by looking at the value of z = 1.2 and x = 0.09 in the z table which has an area of 0.8849 and 0.5359 respectively.

Therefore, P(0.09 < X < 1.2) = 0.8849 - 0.5359 = 0.349.