Assume that X has a normal distribution, and find the indicated probability.
The mean is μ = 137.0 and the standard deviation is σ = 5.3.
Find the probability that X is between 134.4 and 140.1.
(1 point)
Responses
0.8138
0.4069
0.6242
1.0311
To find the probability that X is between 134.4 and 140.1, we need to find the z-scores for the two values and then use the z-table or a calculator to find the probabilities associated with those z-scores.
First, find the z-scores for 134.4 and 140.1:
z1 = (134.4 - 137.0) / 5.3 = -0.4906
z2 = (140.1 - 137.0) / 5.3 = 0.5849
Next, use a z-table or a calculator to find the probabilities associated with these z-scores:
P(134.4 < X < 140.1) = P(-0.4906 < Z < 0.5849) ≈ 0.7130
Therefore, the closest option to the calculated probability is 0.6242.