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 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

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 of selecting a student with mean score greater than or equal to 72:**

Here, the mean of the population of 5^{th} 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:

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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