Suppose that the walking step lengths of adult males are normally distributed with a mean of 2.5
feet and a standard deviation of 0.5
feet. A sample of 51
men’s step lengths is taken.
Step 2 of 2: Find the probability that the mean of the sample taken is less than 1.9
feet. Round your answer to 4
decimal places, if necessary.
To find the probability that the mean of the sample taken is less than 1.9 feet, we need to first calculate the standard error of the mean and then use the Z-score formula.
Standard error of the mean (SEM) = standard deviation / square root of sample size
SEM = 0.5 / √51 ≈ 0.0707
Now, we calculate the Z-score:
Z = (sample mean - population mean) / SEM
Z = (1.9 - 2.5) / 0.0707
Z ≈ -8.47
Using a Z-table or calculator, we find that the probability corresponding to a Z-score of -8.47 is very close to 0.
Therefore, the probability that the mean of the sample taken is less than 1.9 feet is approximately 0.