Expected Values and Standard Deviation

Professional golfer John Daly is known for his long drives off the tee. Suppose his drives have a mean distance of 315 yards with a standard deviation of 12 yards. What lengths of drives will constitute the middle 60% of all of his drives?

• 303 yards to 327 yards

• 0 to 318 yards

• 312 yards to 318 yards

• 305 to 325 yards

The distances male long jumpers for State College jump are approximately normal with a mean of 263 inches and a standard deviation of 14 inches.  
Suppose a male long jumper's jump ranked in the 75th percentile.  How long was his jump?

• 0.67 inch

• 263 inches

• 272.44 inches

• 277.25 inches

Alex's baby was in the 96th percentile for height when she was born. Given σ = 2 inches, and µ = 20 inches, how long was Alex's baby when she was born?

• 23.5 inches

• 20.15 inches

• 17.45 inches

• 37 inches

What term is used to describe the average value of a discrete random variable over numerous trials of an experiment?

• mean

• probability

• standard deviation

• variance

Which of the following represents the amount of spread, dispersion, or variability of the items in a distribution?

• mean or expected value

• median and mode

• outcomes and probability distribution

• variance and standard deviation

How would you interpret a very small variance or standard deviation but not equal to zero?

• The values of the random variables are farther from the mean.

• The values of the random variables are nearer to the mean.

• The values of the random variables are equal to the mean.

• The values of the random variables have no relationship with the mean.

What formula is described by σ² = ∑[x² * P(x)] − u²?

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Which of the following represents the mean value of a discrete random variable?

• Expected value

• Median

• Standard deviation

• Standard deviation

Which of the following is the correct formula to find the expected value of the probability distribution?

• E(x) = ∑[x ∙ P(x)]

• E(x) = ∑[x²∙ P(x)]

• E(x) = ∑[x² ∙ P(x)] − u²

Which of the following rules state that almost all data fall within the 1, 2, and 3 Standard Deviation of the Mean when the population is normally distributed?

• Empirical rule

• Lottery rule

• Pascal’s triangle rule

• Sampling rule