1. In the 19th century, most books quoted "blood heat" as 98 F, until a study...

1. In the 19th century, most books quoted "blood heat" as 98 F, until a study published the mean (but not the variance) of a large sample as 36.88 °C. Subsequently, that mean was widely quoted as "37 C”. This translates to 98.6 F. (Wikipedia)

In a recent study of 148 healthy men and women ages 18-40 years, participating in the Shigella Vaccine Trials at the University of Maryland Center for Vaccine Development, had oral temperatures measured 1-4 times daily for three consecutive days using an electronic digital thermometer. The mean observed oral temperature was 36.8 C which translates to 98.2 F, with a standard deviation of 0.62 F. (Altern Med Rev 2006;11(4):278-293)

If you select a person at random from a population with body temperatures that are N(98.2,0.62)…-

. Use the empirical rule to determine the probability that the body temperature is between 98.2 and 99.44. Round to 4 decimal places

In the 19th century, most books quoted "blood heat" as 98 F, until a study published the mean (but not the variance) of a large sample as 36.88 °C. Subsequently, that mean was widely quoted as "37 C”. This translates to 98.6 F. (Wikipedia)
In a recent study of 148 healthy men and women ages 18-40 years, participating in the Shigella Vaccine Trials at the University of Maryland Center for Vaccine Development, had oral temperatures measured 1-4 times daily for three consecutive days using an electronic digital thermometer. The mean observed oral temperature was 36.8 C which translates to 98.2 F, with a standard deviation of 0.62 F. (Altern Med Rev 2006;11(4):278-293)
If you select a person at random from a population with body temperatures that are N(98.2,0.62)…
-. Use the empirical rule to determine the probability that the body temperature is between 97.58 and 99.44. Round to 4 decimal places

If you select a person at random from a population with body temperatures that are N(98.2,0.62)…-

- Use the empirical rule to determine the probability that the body temperature is larger than 99.44. Round to 4 decimal places

Solutions

Expert Solution

We are given the following data, using this we find the empirical distribution as shown

We can put this in a diagram as follows

1. Use the empirical rule to determine the probability that the body temperature is between 98.2 and 99.44. Round to 4 decimal places

We need to find the probability of the highlighted area of the curve which is equal to = 0.3413 + 0.1359 = 0.4772 (approx. 0.475)

2.Use the empirical rule to determine the probability that the body temperature is between 97.58 and 99.44. Round to 4 decimal places

We need to find the probability of the highlighted area of the curve which is equal to = 0.3413+0.3413 + 0.1359 = 0.8185
(approx. 0.815)

3.Use the empirical rule to determine the probability that the body temperature is larger than 99.44. Round to 4 decimal places

We need to find the probability of the highlighted area of the curve which is equal to = 0.0214+0.0135=0.0344
(which is approximately 0.035)

orchestra answered 1 year ago

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