Question

a normal distribution has a mean of 4 and a standard deviation of 1. what percent of values are from 4 to 7? (type an integer or a decimal)

Explanation:

Step1: Calculate z-scores for 4 and 7

For $x=4$: $z_1=\frac{4-4}{1}=0$
For $x=7$: $z_2=\frac{7-4}{1}=3$

Step2: Find corresponding probabilities

$P(Z \leq 0) = 0.5$, $P(Z \leq 3) \approx 0.9987$

Step3: Compute the difference

$P(0 \leq Z \leq 3) = 0.9987 - 0.5 = 0.4987$

Step4: Convert to percentage

$0.4987 \times 100 = 49.87$

Answer:

49.87