Carly is the principal at a middle school and wants to know the average IQ of all the female, seventh-grade students. She does not know anything about what the population distribution looks like. She took a simple random sample of 31 seventh-grade girls in her school and found the average IQ score in her sample was 105.8 and the standard deviation was 15. Assume that all conditions are met, construct the 96% Confidence interval for the average IQ score of all seventh-grade girls in the school.

The 96% confidence interval for the average IQ score of all seventh-grade girls in the school is (105, 111.6).

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 31 - 1 = 30

96% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 30 degrees of freedom(y-axis) and a confidence level of . So we have T = 2.15

The margin of error is:

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 105.8 - 5.8 = 105.

The upper end of the interval is the sample mean added to M. So it is 105.8 + 5.8 = 111.6

The 96% confidence interval for the average IQ score of all seventh-grade girls in the school is (105, 111.6).

one that is bigger than 3 1/2

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet