The lifetime of a brand of flashlight is normally distributed with a
mean of 45 hours and standard deviation of 5 hours. Let X be the lifetime of a randomly selected flashlight battery
of this brand. Then the 𝑃𝑃(40 < X < 50) is not equal to
To find the probability P(40 < X < 50), we need to find the z-scores for 40 and 50, and then find the area under the normal curve between these two z-scores.
First, let's find the z-score for 40:
z = (40 - mean) / standard deviation
z = (40 - 45) / 5
z = -1
Next, let's find the z-score for 50:
z = (50 - mean) / standard deviation
z = (50 - 45) / 5
z = 1
Now, we can use a z-table or a calculator to find the area under the normal curve between -1 and 1. The area corresponds to the probability P(40 < X < 50).
Using a z-table, we find that the area under the normal curve between -1 and 1 is approximately 0.6827.
Therefore, the probability P(40 < X < 50) is approximately 0.6827.
So, the statement "the P(40 < X < 50) is not equal to..." is incorrect. The probability is equal to approximately 0.6827.