We have the survey data on the body mass index (BMI) of 651 young women. The mean BMI in the sample was x = 28.9. We treated these data as an SRS from a Normally distributed population with standard deviation σ = 7.2. Give confidence intervals for the mean BMI and the margins of error for 90%, 95%, and 99% confidence. (Round your answers to two decimal places.)

90% confidence

So on this case the 90% confidence interval would be given by (28.44;29.36)    

95% confidence

So on this case the 95% confidence interval would be given by (28.35;29.45)    

99% confidence

So on this case the 99% confidence interval would be given by (28.17;29.63)  

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

represent the sample mean

population mean (variable of interest)

represent the population standard deviation

n=651 represent the sample size  

90% confidence

The confidence interval for the mean is given by the following formula:

  (1)

Since the Confidence is 0.90 or 90%, the value of and , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that

Now we have everything in order to replace into formula (1):

So on this case the 90% confidence interval would be given by (28.44;29.36)    

95% confidence

Since the Confidence is 0.95 or 95%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that

Now we have everything in order to replace into formula (1):

So on this case the 95% confidence interval would be given by (28.35;29.45)    

99% confidence

Since the Confidence is 0.99 or 99%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that

Now we have everything in order to replace into formula (1):

So on this case the 99% confidence interval would be given by (28.17;29.63)  

idk lol xd

step-by-step explanation:

ez do it yourself lazy