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Answer :
Final answer:
To determine the probability that the mean body temperature of 19 people is less than 98.5, we calculate the standard error, find the Z-score for 98.5 using the standard normal distribution, and consult the Z-table to get the probability based on the calculated Z-score.
Explanation:
To find the probability that the mean body temperature of 19 randomly selected people will be less than 98.5, given that human body temperatures are normally distributed with a mean of 98.20 and a standard deviation of 0.62, we'll need to use the Central Limit Theorem and the Z-score formula.
Step 1: Identify the mean (μ) and standard deviation (σ) of the population, which are 98.20 and 0.62 respectively.
Step 2: Calculate the standard error of the mean (SEM) for the sample size n=19.
SEM = σ / √ n = 0.62 / √ 19
Step 3: Use the Z-score formula to find the Z-score for the sample mean of 98.5.
Z = (X - μ) / SEM
where X is the sample mean (98.5).
Step 4: Look up the Z-score in the standard normal distribution table to find the probability.
Assuming the calculation yields a Z-score, the lookup in the standard normal distribution table will give us the probability that the mean temperature of the sample is less than 98.5.
Remember, because the sample size is under 30, we should apply the t-distribution if the population standard deviation is unknown. However, in the provided scenario, we are using the population standard deviation, so the normal distribution is appropriate.
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