Random Variable and Probability Distribution, Mean and Variance

Classify the following random variables as discrete or continuous.

• Discrete

• Continuous

Determine the values of the random variables in each of the following distributions.

Two coins are tossed. Let T be the number of tails that occur. Determine the values of the random variable T.

• 0

• 1

• 2

• 0,1,2

What is another name for normal distribution?

• Gaussian distribution

• Poisson distribution

• Bernoulli’s distribution

• Probability distribution

A group of 625 students has a mean age of 15.8 years with a standard deviation of 0.6 years. The ages are normally distributed. What is the probability that a randomly selected student is older than 16.5 years old?

• 0.864

• 0.879

• 0.121

• None of these

The mean and standard deviation of a population are 400 and 40, respectively. Sample size is 25. 
What is the mean of the sampling distribution?

• 400

• 40

• 25

• 8

The mean and standard deviation of a population are 400 and 40, respectively. Sample size is 25. 
What is the standard error of the sampling distribution?

• 400

• 40

• 25

• 8

These symbols represent the mean and standard deviation for which of the following distributions?

• The Population

• The Sample

• The Sampling Distribution

The amount of fuel used by jumbo jets to take off is normally distributed with a mean of 4000 gallons and a standard deviation of 125 gallons.  What is the probability that the mean number of gallons of fuel needed to take off for a randomly selected sample of 40 jumbo jets will be less than 3950 gallons?

• .0057

• .025

• .345

• .781

Researches found that boys playing high school football absorb an average of 355 hits to the head with a standard deviation of 80 hits during a season.  What is the probability on a randomly selected team of 48 players that the average number of head hits per player is between 340 and 360?

• .236

• .429

• .571

• .614

Suppose the teenagers that attend public high schools get an average of 5.7 hours of sleep each night with a standard deviation of 1.7 hours.  What is the probability that a randomly selected group of 35 high school students get more than 6 hours of sleep each night?

• .430

• .148

• .281

• .087