Question

Suppose you are working with a data set that is normally distributed, with a mean of 200 and a standard deviation of 47. Determine the value of x from the following information. 60% of the values are greater than x. x is below 17% of the values. 22% of the values are less than x. x is greater than 55% of the values.

Answer 1

Answer:

That is, 60% of the values are greater than 188.25

244.18 is below 17% of the values

22% of the values are less than 163.81

205.64 is greater than 55% of the values

step-by-step explanation:

Use the standard normal distribution table attached.

- 60% of the values are greater than x is equivalent to find Z = 40% = 0.4 (that is, the right tail has 60% of the area in it). In this case:

Z = -0.25

Z is computed as follows:

Z = (x - mean)/standard deviation

Replacing:

-0.25 = (x - 200)/47

x = -0.25*47 + 200 = 188.25

-  x is below 17% of the values. That is equivalent to: right-tail has 17% of the area. To get this, find Z which are is 0.17 and multiply it by -1, then, solve to find x:

Z = -0.94

0.94 = (x - 200)/47

x = 0.94*47 + 200 = 244.18

- 22% of the values are less than x. That is equivalent to: left tail of 22%. From the figure we see that correspond to Z = -0.77. Therefore:

-0.77 = (x - 200)/47

x = -0.77*47 + 200 = 163.81

- x is greater than 55% of the values. That is equivalent to: left tail of 55%. To get this, find Z with 45% in the table, which is -0.12, multiply it by -1, which makes Z = 0.12. Then:

0.12 = (x - 200)/47

x = 0.12*47 + 200 = 205.64