Question

Hi! If you can help me answer these questions and explain why. I am having a hard time understanding how and why.

A bell-shaped data set has a mean of 50 and a standard deviation of 5.

1.) ___________ percent of the data lie between 45 and 55.

2.) 95 percent of the data lie between _______ and ________.

3.) ___________ percent of the data lie between 50 and 55.

4.) The z-score for the data value 53 is _________.

Answer 1

Given that

1)

Here we have

According to empirical rule, 68% data values lie within one standard deviation of mean.

Answer: 68%

2)

According to empirical rule, 95% data values lie within 2 standard deviations of mean. The required interval is

3)

The percent of data values lie between 45 and 55 is 68% so percent of data lie between 50 and 55 is

68% / 2 = 34%

4)

The z-score for the data value 53 is