The lifetime of a brand of flashlight is normally distributed with a mean of 40 hours and a standard deviation of 10 hours. Let X be the lifetime of a randomly selected flashlight battery of this brand. Then the P(40<X<50) is equal to
To solve this, we need to calculate the z-scores for both 40 and 50, and then find the area under the normal curve between those z-scores.
The z-score for 40 hours can be calculated as:
z = (X - μ) / σ
z = (40 - 40) / 10
z = 0
The z-score for 50 hours can be calculated as:
z = (X - μ) / σ
z = (50 - 40) / 10
z = 1
Now, we need to find the area under the normal curve between these two z-scores. We can use a standard normal distribution table or a calculator to find this area.
Using a standard normal distribution table, the area to the left of z = 0 is 0.5000, and the area to the left of z = 1 is 0.8413. Therefore, the area between these two z-scores is:
0.8413 - 0.5000 = 0.3413
Therefore, P(40 < X < 50) is equal to 0.3413 or 34.13%.