Obesity is a risk factor for many health problems such as type 2 diabetes, high blood pressure, joint problems, and gallstones. Using data collected in 2018 through the National Health and Nutrition Examination Survey, the National Institute of Diabetes and Digestive and Kidney Diseases estimates that 37.7% of all adults in the United States have a body mass index (BMI) in excess of 30 and so are categorized as obese. The data in the file Obesity are consistent with these findings. BMI:

16.2 46.8 39 13.6 31.3
31.1 36.7 29 34.2 7.4
24.8 32.4 41 34.8 30.8
23.8 38 16 21.2 14
8 26.1 320 31 37.8
24 39.2 26 31.3 32
38.8 23.8 524 35 20.4
51.5 23.4 17 27.5 19.8
28 27.9 33 422 45.7
26.5 44.6 30 37.8 56.3
43.1 27.5 23 49.5 22.9
18.7 35.3 19 31.2
28.2 34.5 24 29
17.9 25.6 11 26.1
33.1 27.3 11 26.5
25.6 28 29 25.5

Requried:
a. Use the Obesity data set to develop a point estimate of the BMI for adults in the United States. (Round your answer to two decimal places.) Are adults in the United States obese on average?
b. What is the sample standard deviation? (Round your answer to four decimal places.)
c. Develop a 95% confidence interval for the BMI of adults in the United States. (Round your answers to two decimal places.)

a. A point estimate of the BMI for adults in the United States can be calculated from the sample mean, which has a value M=44.57.

b. The sample standard deviation is s=79.9507.

c. The 95% confidence interval for the BMI of adults in the United States is (26.18, 62.96).

Step-by-step explanation:

We start by calculating the sample mean and standard deviation of the BMI data:

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=44.57.

The sample size is N=75.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

The degrees of freedom for this sample size are:

The t-value for a 95% confidence interval and 74 degrees of freedom is t=1.993.

The margin of error (MOE) can be calculated as:

Then, the lower and upper bounds of the confidence interval are:

The 95% confidence interval for the BMI of adults in the United States is (26.18, 62.96).

step-by-step explanation:

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq