Q.6.35 - Elementary Statistics

Question

 Female College Students. Refer to Example 6.3 on page 256 .

a. Use the relative-frequency distribution in Table 6.1 to obtain the percentage of female students who are between  $60 and 65$inches tall.

b. Use your answer from part (a) to estimate the area under the normal curve having parameters $\mu =64.4 and \sigma =2.4$ that lies between $60 and 65$ . Why do you get only an estimate of the true area?

Step-by-Step Solution

Answer

(a) The percentage of female students who are between  $60 and 65$inches  is$55.70\%$

(b) The area under the associated normal curve between $60 and 65$ is$0.5570$

Part (a) Step 1: Given Information

The given table is:

we have to find the percentage of female students who are between $60 and 65$ inches tall.

Part (a) Step 2: Explanation

Consider the classes

60-61

61-62

62-63

63-64

64-65

The percentage of kids who are between $60$ and $65$ inches tall can be calculated by multiplying the relative frequencies as follows:

$0.0450+0.0757+0.1170+0.1480+0.1713=0.5570$

As a result, the percentage of students between the ages of $60$ and $65$ is $55.70$ percent.

Part (b) Step 1: Given Information

We have To estimate The area under the normal curve having parameters $\mu =64.4 and \sigma =2.4$.

Part (b) Step 2: Explanation

The students' heights are roughly evenly divided in this group. So, between $60 and 65$, the area under the related normal curve is $0.5570$.

We can only acquire an estimate of the true area because the students heights are somewhat regularly distributed.