To solve this problem, we can calculate the z-score for a sample mean of 1550 hours using the formula:
z = (X̄ - μ) / (σ / √n)
where:
X̄ = sample mean (1550 hours)
μ = population mean (1600 hours)
σ = population standard deviation (400 hours)
n = sample size (64 bulbs)
Plugging in the values:
z = (1550 - 1600) / (400 / √64)
z = -50 / 50
z = -1
Now, we look up the z-score of -1 in a standard normal distribution table to find the probability that the sample mean lifetime is more than 1550 hours. The area to the left of z = -1 is 0.1587, so the probability to the right (more than 1550 hours) is 1 - 0.1587 = 0.8413.
Therefore, the probability that the sample mean lifetime is more than 1550 hours is 0.8413.
Therefore, answer is:
0.8413
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. What is the probability that the sample mean lifetime is more than 1550 hours?
0.9616
0.9242
0.8413
0.7686
1 answer
1 answer