# Normal Distribution and Values

The incomplete table at right is a discrete random variable x's probability distribution, where x is the number of courses taken by randomly selected undergraduate student. (Please refer to attached document to view the table and note that the questions are written in the excel file as well ) Answer the following:

(a) Determine the value that is missing in the table.

(b) Explain the meaning of P(x ? 2) as it applies to the context of this problem.

(c) Determine the value of P(x ? 2).

(d) Find the probability that x is at least 3.

(e) Find the mean (expected value) and standard deviation of this probability distribution.

(f) Create an example probability distribution to the right in which the expected value is 5. (You must have at least three different values for x)

Nationwide, 68% of American adults own a cell phone. Let us define "owning a cell phone" as the desired trait within a study and suppose that a random sample of 5 American adults is taken. Answer the following questions that pertain to this situation.

(a) Recognizing that this is a binomial situation, give the meaning/values of S, F, n, p, and q.

S is: n =

F is: p =

q =

(b) Construct the complete binomial probability distribution for this situation in a table at right.

(c) Find the probability that all 5 of the people from the collected random sample will own a cell phone.

(d) Find the probability that more than 2 people from the sample will own a cell phone.

(e) Find the mean and standard deviation of this binomial probability distribution.

(f) By writing a sentence, interpret the meaning of the mean value found in (e).

Answer the following:

(a) What are the values for the mean and standard deviation on a standard normal curve?

(b) What are considered unusual z-score values?

With regards to a standard normal distribution complete the following:

(a) Find P(z > 0), the percentage of the standard normal distribution above the z-score of 0.

(b) Find P(z < 1), the percentage of the standard normal distribution below the z-score of 1.

(c) Find P(-1.23 < z < 0.5).

(d) Find P( z > -3).

(e) Find the z-score that separates the lower 25% of standarized scores from the top 75% . . . that is find the z-score corresponding to P25.

#### Solution Summary

The expert examines normal distributions and values. The percentages of the standard normal distributions are determined.