STAT 2060 Lecture Notes - Lecture 7: Standard Deviation, Probability Distribution, Binomial Distribution

A  Compute and interpret the mean of the random variable x

B Compute the standard deviation of the random variable x.

C. What is the probability that a randomly selected student has a parent involved in three activities?

D  What is the probability that a randomly selected student has a parent involved in three or four activities?

E.

In the following probability distribution, the random variable x represents the number of activities a K to the 5th-grade student is involved in.

Complete parts (a) through (f) below.

   x           0              1               2               3               4

P(x)      0.299       0.145         0.234        0.053         0.269

(a) Verify that this a discrete probability distribution.

The probability distribution of the random variable X represents the number of hits a baseball player obtained in a game for the 2012 baseball season

The probability distribution was used along with statistical software to simulate 25 repetitions of the experiment (25 games). The number of hits was recorded. Approximate the mean and standard deviation of the random variable X based on the simulation. The simulation was repeated by performing 50 repetitions of the experiment. Approximate the mean and standard deviation of the random variable. Compare your results to the theoretical mean and standard deviation. What property is being illustrated?

a.Compute the theoretical mean of the random variable X for the given probability distribution.

Meu = ?

b. Compute the theoretical standard deviation of the random variable X for the given probability distribution.

Sigma =?

c.Approximate the mean of the random variable X based on the simulation for 25 games.

Xbar=?

d. Approximate the standard deviation of the random variable X based on the simulation for 25 games.

S=?

The probability distribution of the random variable X represents the number of hits a baseball player obtained in a game for the 2012 baseball season x P(x) 0 0.167 1 0.3289 2 0.2801 3 0.149 4 0.0382 5 0.0368 The probability distribution was used along with statistical software to simulate 25 repetitions of the experiment (25 games). The number of hits was recorded. Approximate the mean and standard deviation of the random variable X based on the simulation. The simulation was repeated by performing 50 repetitions of the experiment. Approximate the mean and standard deviation of the random variable. Compare your results to the theoretical mean and standard deviation. What property is being illustrated? a.Compute the theoretical mean of the random variable X for the given probability distribution. Meu = ? b. Compute the theoretical standard deviation of the random variable X for the given probability distribution. Sigma =? c.Approximate the mean of the random variable X based on the simulation for 25 games. Xbar=? d. Approximate the standard deviation of the random variable X based on the simulation for 25 games. S=?