The distribution of the scores on a certain exam is N30 10 w

The distribution of the scores on a certain exam is N(30, 10), which means that the exam scores are Normally distributed with a mean of 30 and standard deviation of 10. a. Sketch the curve and label, on the x-axis, the position of the mean, the mean plus or minus one standard deviation, the mean plus or minus two standard deviations, and the mean plus or minus three standard deviations. b. Find the probability that a randomly selected score will be less than 20. Shade the region under the Normal curve whose area corresponds to this probability. a. Choose the correct graph below. b. What is the probability that a randomly selected score will be less than 20? Using the Empirical Rule, the probability that a randomly selected score will be less than 20 is about %. (Type an integer or a decimal.) Which graph shows the distribution with the region shaded under the Normal curve whose area corresponds to the probability that a randomly selected score is less than 20?

Solution

a)

N(30,10) implies that

the mean = 30 and standard deviation = 10

In a normal distribution graph mean is the center of the graph

and sigma = 10

so the correct choice is A)

b)

P(X<20) = P(Z < 20 -mean/standard deviation)

= P(Z < 20-30/10)

= P(Z<-1)

= 0.1587

c)

the corresponding shaded region will be the area of graph where u<20

or the area is approximately 15% of the area overed under the curve

so, the correct choice is A)