Question

normal curves
question 1
a normal distribution has a mean of 40 and a standard deviation of 2. the area under the curve to the left of 39 is 0.3085. what is the area under the curve to the right of 39?
a. 0.1915
b. 0.3085
c. 0.6915
d. 0.9332
question 2
the area under a normal curve to the left of 39 is 0.3085, and the area to the left of 43 is 0.9332. what is the area between 39 and 43?
a. 0.2415
b. 0.6247
c. 0.6915
d. 1.2417
question 3
a data set is normally distributed with mean 75 and standard deviation 8. approximately what proportion of the data falls within one standard deviation of the mean (between 67 and 83)?
a. 50%
b. 68%
c. 95%
d. 99.7%

Explanation:

Question 1

Step1: Total area under curve = 1

Total area = $1$

Step2: Subtract left area from total

Area right of 39 = $1 - 0.3085$

Question 2

Step1: Subtract left areas

Area between 39 & 43 = $0.9332 - 0.3085$

Question 3

Step1: Apply empirical rule

Proportion within 1 SD = $68\%$

Answer:

Question 1: C. 0.6915
Question 2: B. 0.6247
Question 3: B. 68%