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Assume the random variable x is normally distributed with mean
muequals80
and standard deviation
sigmaequals5.
Find the indicated probability.

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Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

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1. Assume the readings on thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. Find the probability that a randomly selected thermometer reads greater than −1.59 and draw a sketch of the region.

2. Assume the readings on thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. Find the probability P(−0.45<z<0.45)​, where z is the reading in degrees.

P(−0.45<z<0.45)=____________

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=?

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=?

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