For 261 female heights, the mean was 66.3 inches and the standard deviation was

Question

For 261 female heights, the mean was 66.3 inches and the standard deviation was 3.2 inches. The shortest person in this sample had a height of 5s inches (a) Find the z-score for the height of 55 inches (3 decimal places) (b) What does the (positive or negative) sign for the a-score represent? The height is above the mean. The height is below the mean. The height is a potential outlier. The height is not a potential outer (e) Assuming the distribution of heights is approximately bell-shaped, is this observation a potential outlier according to the three standard deviation distance criterion? Explain. O Yes, it is less than 3 standard deviations away from the mean. O Yes, is more than 3 standard deviations away from the mean. O No, it is less than 3 standard deviations away from the mean. O No, it is more than 3 standard deviations away from the mean

Explanation / Answer

Z=x-mean/sd

given mean=66.3

sd=3.2

for x=55

z=55-66.3/3.2

z=-3.531

ANSWER:-3.531

Solutionb:

As z value is negative

it is 3.532 standard devaitions below mean

THE HEIGHT IS BELOW THE MEAN

Solutionc

mean-3sd=66.3-3*3.2=56.7

mean+3sd=66.3+3*3.2=75.9

50 is below the range of 56.7 and 75.9

less than 3 deviations from mean

YES IT IS LESS THAN 3 STANDARD DEVIATIONS AWAY FROM THE MEAN

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