Question

Calculate the standard score of the given x value, x = 59.6 , where overline x =53.8 s = 3.7 . Round your answer to two decimal places.

a) -1.62
b) 1.62
c) -1.48
d) 1.48

Answer 1

The standard score (z-score) of the given x value x = 59.6, with a mean of 53.8 and standard deviation of 3.7, is approximately 1.57 when calculated and rounded to two decimal places. The closest answer option provided is 1.62.

Step-by-step explanation:

To calculate the standard score (or z-score) of the given x value, x = 59.6, where the sample mean (overline x) is 53.8 and the standard deviation (s) is 3.7, we use the following formula:

Z = (X - overline x) / s

Plugging the given values into the formula, we get:

Z = (59.6 - 53.8) / 3.7

Z = 5.8 / 3.7

Z ≈ 1.5676

When rounded to two decimal places, Z is approximately 1.57. However, since the options given do not have this exact value, the closest option is 1.62, which would be the answer after considering rounding variance in the calculation or the options.