To find the probability that the sample mean lifetime is more than 1550 hours, we need to convert the sample mean to z-score 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)
z = (1550 - 1600) / (400 / √64)
z = -50 / 50
z = -1
Now, we look up the z-score of -1 in the standard normal distribution table, which corresponds to a probability of 0.1587. However, since we're interested in the probability that the sample mean is MORE than 1550 hours, we need to find the area to the right of the z-score of -1.
P(z > -1) = 1 - P(z < -1)
P(z > -1) = 1 - 0.1587
P(z > -1) = 0.8413
Therefore, the probability that the sample mean lifetime is more than 1550 hours is 0.8413.
he 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
0.5624
1 answer