The lifetimes of a certain brand of light bulbs are known to be normally distributed with a mean of 1600 hours and a standard deviation of 400 hours. A random sample of 64 of these light bulbs is taken. The probability is 0.1492 that the sample mean lifetime is more than how many hours
To find the number of hours that the sample mean lifetime is more than, we first need to calculate the standard error of the sample mean. The standard error of the sample mean is given by the formula:
Standard Error = (standard deviation) / √(sample size)
Standard Error = 400 / √64 = 400 / 8 = 50
Next, we need to find the z-score corresponding to a probability of 0.1492. This z-score can be found using a standard normal distribution calculator or table. The z-score corresponding to a probability of 0.1492 is approximately -1.075.
Finally, we can use the formula for z-scores to find the number of hours that corresponds to the z-score of -1.075:
z = (X - μ) / Standard Error
-1.075 = (X - 1600) / 50
-1.075(50) = X - 1600
-53.75 = X - 1600
X = 1600 - 53.75 = 1546.25 hours
Therefore, the probability is 0.1492 that the sample mean lifetime is more than 1546.25 hours.