A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The probability that the sample mean will be less than 82 minutes is
0.7734
To find the probability that the sample mean will be less than 82 minutes, we need to use the standard normal distribution. First, we calculate the standard error of the mean:
Standard error = standard deviation / sqrt(sample size)
Standard error = 40 / sqrt(64)
Standard error = 5
Next, we calculate the z-score for a sample mean of 82 minutes:
z = (sample mean - population mean) / standard error
z = (82 - 80) / 5
z = 0.4
Using a standard normal distribution table or calculator, we find that the probability of a z-score less than 0.4 is 0.6554.
Therefore, the probability that the sample mean will be less than 82 minutes is 0.6554 or 65.54%.