answer the question below. type your response in the space provided. consider a normally distributed data…

answer the question below. type your response in the space provided. consider a normally distributed data set with a mean of 75 and a standard deviation of 5. if one of the recorded values is 87, how many standard deviations away from the mean is this value? enter your answer up to one decimal place.

answer the question below. type your response in the space provided. consider a normally distributed data set with a mean of 75 and a standard deviation of 5. if one of the recorded values is 87, how many standard deviations away from the mean is this value? enter your answer up to one decimal place.

Answer

Explanation:

Step1: Recall z - score formula

The formula for the z - score (number of standard deviations from the mean) is $z=\frac{x-\mu}{\sigma}$, where $x$ is the data - point, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Identify values

We are given that $\mu = 75$, $\sigma=5$, and $x = 87$.

Step3: Calculate z - score

Substitute the values into the formula: $z=\frac{87 - 75}{5}=\frac{12}{5}=2.4$.

Answer:

2.4