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Suppose that human body temperatures are normally distributed with a mean of 98.2 degrees F and a standard deviation of 0.62 degrees F.

1. Physicians want to select the lowest body temperature considered to be a fever and decide that only 5% of the population should exceed this temperature. What value should they use for this temperature?

2. Suppose that one individual is selected at random. Find the probability that their temperature will exceed 100 degrees F.

3. Suppose that 4 individuals are selected at random. Find the probability that the sample mean will exceed 98.7 degrees F.

Answer :

1. The physicians should use temperature of 99.2 degrees. 2. F is approximately 0.002 or 0.2%. 3. The probability that sample mean of 4 individuals will exceed 98.7 degrees F is approximately 0.053 or 5.3%.

Using a standard normal distribution table or a calculator with normal distribution function. Then, use formula:

[tex]z = (x - \mu) / \sigma[/tex]

Solving for x, we get:

[tex]x = z * \sigma + \mu[/tex]

[tex]x = 1.645 * 0.62 + 98.2[/tex]

x ≈ 99.2

2. We can use same formula as in 1, but this time we want to find probability.

[tex]z = (x - \mu) / \sigma[/tex]

Solving for z:

[tex]z = (100 - 98.2) / 0.62[/tex]

z ≈ 2.90

We can find probability that z-score is greater than 2.90, which is approximately 0.002.

3. Mean of sample means = μ = 98.2

standard deviation of sample means = [tex]\sigma / sqrt(n) = 0.62 / sqrt(4) = 0.31[/tex]

Using the standard normal distribution table:

[tex]z = (98.7 - 98.2) / 0.31[/tex]

z ≈ 1.61

To know more about standard normal distribution, here

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