Question

question 20 of 25
suppose a normal distribution has a mean of 62 and a standard deviation of 4. what is the probability that a data value is between 57 and 65? round your answer to the nearest tenth of a percent.
a. 68.8%
b. 66.8%
c. 67.8%
d. 69.8%

Explanation:

Step1: Calculate z-scores

$z_1 = \frac{57 - 62}{4} = -1.25$, $z_2 = \frac{65 - 62}{4} = 0.75$

Step2: Find cumulative probabilities

$P(Z < -1.25) ≈ 0.1056$, $P(Z < 0.75) ≈ 0.7734$

Step3: Compute the difference

$0.7734 - 0.1056 = 0.6678$

Step4: Convert to percentage

$0.6678 × 100 ≈ 66.8\%$

Answer:

B. 66.8%