# All California 5th graders take a standardized test. The mean for the population of 5th graders is 68.9 and the standard deviation for the population is 10. What is the probability of randomly selecting a student who scored a. ≥ 85?b. less than or equal to 85?c. between 80 & 85?d. between 60 & 85?

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All California 5th graders take a standardized test. The mean for the population of 5th graders is 68.9 and the standard deviation for the population is 10. What is the probability of randomly selecting a student who scored

a. ≥ 85?

b. less than or equal to 85?

c. between 80 & 85?

d. between 60 & 85?

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Step 1

If a random variable X has a distribution with mean µ and standard deviation σ, then the Z-score is defined as,

Step 2

a.The probability that the student scored greater than or equal to 85 points:

Here, the mean of the population of 5th graders is 68.9 and the standard deviation is 10.

Let X be the score obtained by the student for the test.

The probability that the randomly selected student scored greater than or equal to 85 points is 0.0537 and is obtained as shown below:

Step 3

b.The probability that the student scored less than or equal to 85 points:

The probability that the randomly selected studen...

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