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StatisticsQ&A LibraryAll 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?Question

Asked May 5, 2019

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All California 5^{th} graders take a standardized test. The mean for the population of 5^{th} 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 5^{th} 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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