Question

Approximately 30.4% of U.S. adults 25 years and older have high school degrees as their highest level of education. Suppose 100 such adults are selected at random and they are asked if a high school degree is their highest level of education. Let X be the result that the highest level of education is a high school diploma.

A) What is p(probability of success) and N(the number of trials) that define this binomial experiment?

B) What are the mean and standard deviation of the Normal distribution that can be used to approximate this Binomial experiment?

C) Determine the probability that the number of who have a high school diploma as their highest level of education is exactly 32.  

D) Determine the probability that the number of who have a high school diploma as their highest level of education is between 30 and 35.

E) Determine the probability that the number of who have a high school diploma as their highest level of education is greater than 30.  

Answer 1

A) Probability of success, p = 0.304

Number of trials, n = 100

B) For Normal distribution that can be used to approximate this Binomial experiment,

Mean = np

= 100 x 0.304

= 30.4

Standard deviation =

=

= 4.60

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

P(exactly 32) = P(X = 32)

= P(X < 32.5) - P(X < 31.5)

= P(Z < (32.5 - 30.4)/4.6) - P(Z < (31.5 - 30.4)/4.6)

= P(Z < 0.46) - P(Z < 0.24)

= 0.6772 - 0.5948

= 0.0824

D) P(between 30 and 35) = P(30 X 35)

= P(X < 35.5) - P(X < 29.5)

= P(Z < (35.5 - 30.4)/4.6) - P(Z < (29.5 - 30.4)/4.6)

= P(Z < 1.11) - P(Z < -0.20)

= 0.8665 - 0.4207

= 0.4458

E) P(greater than 30) = 1 - P(X < 29.5)

= 1 - 0.4207

= 0.5793