Question

question 7
date:
on a standardized test with a normal distribution, the mean score is 500 and the standard deviation is 100.
what proportion of test-takers score between 400 and 600?
a. 34.13%
b. 68.26%
c. 95.44%
d. 99.74%
question 8
a baker knows that the weight of loaves of bread is normally distributed with a mean of 500 grams and a standard deviation of 25 grams. given that the area under the curve to the left of 475 grams is 0.1587, what is the area between 475 and 525 grams?
a. 0.3174
b. 0.6826
c. 0.8413
d. 0.9772

Explanation:

Question 7

Step1: Calculate z-scores

For $X=400$: $z_1=\frac{400-500}{100}=-1$
For $X=600$: $z_2=\frac{600-500}{100}=1$

Step2: Use empirical rule

Proportion for $z=-1$ to $z=1$ is 68.26%

Question 8

Step1: Find right tail area

Area right of 525 = Area left of 475 = 0.1587

Step2: Calculate middle area

$1 - 2\times0.1587=0.6826$

Answer:

Question 7: B. 68.26%
Question 8: B. 0.6826