Final answer:
To find the z score for a temperature of 99.5°F with a mean of 98.20°F and a standard deviation of 0.62°F, we use the formula z = (X - mean) / standard deviation. The z score is then compared to a standard level of significance to determine if the temperature is unusual. In this case, the z score of 2.10 indicates that the temperature of 99.5°F should be considered unusual.
Step-by-step explanation:
To find the z score, we can use the formula:
z = (X - mean) / standard deviation
where X is the value we want to find the z score for. In this case, X = 99.5°F, mean = 98.20°F, and standard deviation = 0.62°F. Plugging these values into the formula:
z = (99.5 - 98.20) / 0.62
z = 2.10
To assess whether this temperature should be considered unusual, we can compare the z score to a standard level of significance. A commonly used level of significance is z = 2 or -2. If the z score is greater than 2 or less than -2, then the temperature can be considered unusual. In this case, the z score is 2.10, which is greater than 2. Therefore, the temperature of 99.5°F should be considered unusual.