Answered

Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Get quick and reliable solutions to your questions from a community of experienced experts on our platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

A large random sample was taken of body temperatures of women at a university. The data from the sample were normally distributed with a mean body temperature of
98.52°F and a standard deviation of 0.727°F. Based on this sample, which percentage is the best estimate of the proportion of all women at this university who have a body
temperature more than 2 standard deviations above the mean?
O 0.30%
O 2.28%
72.70%
O 97.72%

Sagot :

oladayoademosu

The best estimate of the proportion of all women at this university who have a body temperature more than 2 standard deviations above the mean is 2.28%.

Since the sample is normally distributed and has a mean μ = 98.52 F and a standard deviation, σ = 0.727 F and we need to find the percentage of all womenat this university who have a body temperature more than 2 standards deviations above the mean.

The normal distribution

Since the sample is normally distributed, 50% of the sample is below the mean. We have 34% of the sample at 1 standard deviation away from the mean and 47¹/₂% at 2 standard deviations above the mean.

Percentage below 2 standard deviations away from mean

So, the percentage below 2 standard deviations from the mean is 50% + 47¹/₂% = 97¹/₂%.

Percentage above 2 standard deviations away from mean

So, the percentage above 2 standard deviations from the mean is 100% - 97¹/₂% = 2¹/₂% = 2.5 %

Since 2.28 % is the closest to 2.5 % from the options, the best estimate is 2.28 %.

So, the best estimate of the proportion of all women at this university who have a body temperature more than 2 standard deviations above the mean is 2.28%.

Learn more about normal distribution here:

https://brainly.com/question/25800303

Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.