Question

A set of data items is normally distributed with a mean of 100 and a standard deviation of

30. Find the data item in this distribution that corresponds to the given z-score =2.5.
z=2.5 is_______

Answer 1

Step-by-step explanation:

To find the data item that corresponds to a given z-score, we can use the formula:

z = (x - μ) / σ

where:

z is the z-score

x is the data item we're looking for

μ is the mean of the distribution

σ is the standard deviation of the distribution

In this case, we're given the values of μ and σ, and we want to find x when z = 2.5. So we can rearrange the formula to solve for x:

x = z * σ + μ

Substituting the given values, we get:

x = 2.5 * 30 + 100 = 175

Therefore, the data item that corresponds to a z-score of 2.5 in this distribution is 175.

Answer 2

The data item that corresponds to a z-score of 2.5 in a normally distributed data set with a mean of 100 and standard deviation of 30 is 175.

Step-by-step explanation:

Given a data set that is normally distributed with a mean of 100 and a standard deviation of 30, we are asked to find the data item in this distribution that corresponds to a given z-score of 2.5.

To find the data item, we can use the formula: z = (x - mean) / standard deviation.

Plugging in the values, we have: 2.5 = (x - 100) / 30.

Solving for x, we get: x = 2.5 * 30 + 100 = 175.

Therefore, the data item that corresponds to a z-score of 2.5 is 175.