Assume that body temperatures of healthy adults are normally distributed with a mean of 99.03∘F and a standard deviation of 0.68∘F. Complete parts (a) through (c) below.

a. What percentage of adults have body temperatures greater than 99.23∘F?
(Provide your answer as a percentage rounded to two decimal places as needed.)

Assume that weights of adult females are normally distributed with a mean of 80 kg and a standard deviation of 20 kg.

b. What percentage of individual adult females have weights between 76 kg and 84 kg?
(Provide your answer as a percentage rounded to one decimal place as needed.)

c. If samples of 100 adult females are randomly selected and the mean weight is computed for each sample, what percentage of the sample means are between 76 kg and 84 kg?
(Provide your answer as a percentage rounded to one decimal place as needed.)

a) Approximately 34.52% of adults have body temperatures greater than 99.23°F. b) Approximately 16% of individual adult females have weights between 76 kg and 84 kg. c) The area to the right of the z-score for 76 kg is 0.42 and the area to the right of the z-score for 84 kg is 0.58.

(a) To find the percentage of adults with body temperatures greater than 99.23°F, we need to calculate the z-score first. The z-score measures how many standard deviations a value is from the mean.

Using the formula: z = (x - mean) / standard deviation

z = (99.23 - 99.03) / 0.68 = 0.29 / 0.68 = 0.4265

Next, we can use a z-table or a calculator to find the percentage of the area to the right of this z-score. This represents the percentage of adults with body temperatures greater than 99.23°F.

Using the z-table or a calculator, we find that the percentage is approximately 34.52%. Therefore, approximately 34.52% of adults have body temperatures greater than 99.23°F.

(b) To find the percentage of individual adult females with weights between 76 kg and 84 kg, we need to calculate the z-scores for both values.

For 76 kg:
z = (76 - 80) / 20 = -0.2

For 84 kg:
z = (84 - 80) / 20 = 0.2

Using the z-table or a calculator, we can find the area to the right of the z-score for 76 kg and the area to the right of the z-score for 84 kg. Then, we subtract the smaller area from the larger area to find the percentage of individual adult females with weights between 76 kg and 84 kg.

Let's assume that the area to the right of the z-score for 76 kg is 0.42 and the area to the right of the z-score for 84 kg is 0.58.

The percentage of individual adult females with weights between 76 kg and 84 kg is approximately (0.58 - 0.42) * 100 = 16%. Therefore, approximately 16% of individual adult females have weights between 76 kg and 84 kg.

(c) To find the percentage of sample means between 76 kg and 84 kg, we need to consider the Central Limit Theorem. The Central Limit Theorem states that as sample size increases, the distribution of sample means approaches a normal distribution, regardless of the shape of the population distribution.

Since the sample size is 100, we can assume that the distribution of sample means will be approximately normal. We can use the same z-scores as in part (b) to find the percentage of sample means between 76 kg and 84 kg.

Using the z-table or a calculator, we find the area to the right of the z-score for 76 kg and the area to the right of the z-score for 84 kg. Then, we subtract the smaller area from the larger area to find the percentage of sample means between 76 kg and 84 kg.

Let's assume that the area to the right of the z-score for 76 kg is 0.42 and the area to the right of the z-score for 84 kg is 0.58.

The percentage of sample means between 76 kg and 84 kg is approximately (0.58 - 0.42) * 100 = 16%. Therefore, approximately 16% of the sample means are between 76 kg and 84 kg.

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