Question

QUESTION 39.1 POINT

Hugo averages 77 words per minute on a typing test with a standard deviation of 8 words per minute. Suppose Hugo's
words per minute on a typing test are normally distributed. Let X = the number of words per minute on a typing test.
Then, X ~ N(77,8).
This z-score
Suppose Hugo types 76 words per minute in a typing test on Wednesday. The Z-score when x = 76 is
tells you that x = 76 is standard deviations to the (right/left) of the mean,
Correctly fill in the blanks in the statement above.

Answer 1

The Z-score when x = 76 is of -0.125, which tells you that x = 76 is 0.125 standard deviations to the left of the mean.

Explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the z-score of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

X ~ N(77,8).

This means that
`\mu = 77, \sigma = 8`

Z-score when X = 76:

`Z = (X - \mu)/(\sigma)`

`Z = (76 - 77)/(8)`

`Z = -0.125`

Negative means that its to the left of the mean.

The Z-score when x = 76 is of -0.125, which tells you that x = 76 is 0.125 standard deviations to the left of the mean.