Introduction to Statistics

An ecologist studying starfish populations records values for each of the following variables from randomly selected pots on a rocky coastline.

x= the number of starfish in the plot

y= the total weight of starfish in the plot

w= the percent of area in the plot that is covered by barnacles

t = the primary type of rock in the plot

How many of these are continuous random variables and how many are discrete random variables?

• Two continuous, two discrete

• one continuous, three discrete

• two continuous, one discrete and one that is not a random variable

• one continuous, two discrete and one that is not a random variable.

Which of the following is closest to the 28th percentile in the standard normal distribution?

• -0.58

• -0.50

• 0.39

• 0.61

A hat holds a large number of slips of paper, each with a single digit from 1 to 4 on it. Which one of the following is a possible probability distribution for X = the number on a randomly selected slip of paper?

• 
• 
• 
• 

A private school has 25 students in each of grades 1 through 12. The principal randomly selects 1 student from each grade and records whether or not the student is over 5 feel tall. Let X = the number of student sin the sample who are over 5 feet tall. Which of the following requirements for a binomial setting is violated in this case?

• There are two possible outcomes for each trial.

• The trials are independent.

• The probability of " success" is the same for each trial.

• The number of trials is fixed.

The figure shows the density curve that is the probability distribution of a continuous random variable. Seven values are marked on the density curve. Which of the following statements is true?

• The mean of the distribution is E.

• The median of the distribution is C.

• The third quartile of the distribution is D.

• The area under the curve between A and G is 1.

A psychologist studied the number of puzzles that subjects were able to solve in a 5-minute period while listening to soothing music. Let X be the number of puzzles completed successfully by a randomly chosen subject. The psychologist found that X had the following probability distribution shown. What is the probability that a randomly chosen subject completes more than the expected number of puzzles in the 5-minute period while listening to soothing music?

• 0.1

• 0.4

• 0.5

• 0.8

A psychologist studied the number of puzzles that subjects were able to solve in a 5-minute period while listening to soothing music. Let X be the number of puzzles completed successfully by a randomly chosen subject. The psychologist found that X had the following probability distribution shown. The standard deviation of X is 0.9. Which of the following is the best interpretation of this value?

• About 95% of subjects solved between 1.8 puzzles less and 1.8 puzzles more than the mean.

• The typical subject solved an average of 0.9 puzzles.

• The number of puzzles solved by subjects typically differed from the mean by about 0.9 puzzles.

• The number of puzzles solved by subjects typically differed from one another by about 0.9 puzzles.

For the normal distribution shown, the standard deviation is closest to

• 1

• 2

• 3

• 6

In the game Pass the Pigs, a small plastic pig is rolled, and its orientation when it comes to a stop determines the number of points a player scores. Approximately 9% of rolls produce a "trotter". Suppose you roll a pig 10 times. Which of the following expressions represents the probability that you roll exactly 2 trotters?

• (0.09)²(0.91)⁸

• (0.09)²(0.91)¹⁰

• ₁₀C₂(0.09)²(0.91)⁸

• ₈C₂(0.09)²(0.91)⁸

If the heights of a population of men follow a normal distribution, and 99.7% have heights between 5 feet 0 inches and 7 feet 0 inches, what is your estimate of the standard deviation of the heights in this population?

• 1 inch

• 3 inches

• 4 inches

• 6 inches