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Considering the population described in question #1, what is the probability of selecting at random from this population a sample of 20 students with a mean score: a. ≥72?b. between 70 & 72? SAMPLE: 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

Question

Considering the population described in question #1, what is the probability of selecting at random from this population a sample of 20 students with a mean score:

 

a. ≥72?

b. between 70 & 72?

 

SAMPLE: 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

check_circleAnswer
Step 1

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

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Step 2

a.The probability of selecting a student with mean score greater than or equal to 72:

Here, the mean of the population of 5th graders is 68.9 and the standard deviation is 10. A sample (n) of 20 students is selected from the population.

Let X-bar be the mean score obtained by the student for the test.

The probability of selecting a student with mean score greater than or equal to 72 is 0.0823 and is obtained as shown below:

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Step 3

b.The probability of selecting a student with mean score between 70 and 72:

The probability of selecting a student w...

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