Practice Exam

An analyst estimates that the year-end price of a stock has the following probabilities: Stock Price Probability $80 0.1 $85 0.3 $90 0.4 $95 0.2 The stock's price at the end of the year is ______.

$88.50

What are the two key properties of a discrete probability distribution?

0 < or equal to P(X = x) < or equal to 1 and E P(X = xi) =1

The probability P(Z < -1.28) is closest to

0.10

The probability P(Z > 1.28) is closest to

0.10

The waiting time at an elevator is uniformly distributed between 30 and 200 seconds. What is the probability a rider must wait between 1 minute and 1.5 minutes?

0.1765

The average time between trades for a high-frequency trading investment firm is 40 seconds. Assume the time between trades is exponentially distributed. Refer to exhibit 6-4. What is the probability that the time between trades for a randomly selected trade and the one preceding it is more than a minute?

0.2231

Let the time between two consecutive arrivals at a grocery store checkout line be exponentially distributed with a mean of three minutes. Find the probability that the next arrival does not occur until at least four minutes have passed since the last arrival.

0.2636

For any normally distributed random variable with mean u and standard deviation o, the proportion of the observations that fall outside the interval [ u-o, u+o] is closest to _____.

0.3174

Two hundred people were asked if they had read a book in the last month. The accompanying contingency table, cross-classified by age, is produced. Under 30 30+ Yes 76 65 No 24 35 The probability that a respondent read a book in the last month and is at least 30 years old is closest to _____.

0.33

It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that at least one in a random sample of four calculators is defective?

0.3439

Alison has all her money invested in two mutual funds, A and B. She knows that there is a 40% chance that fund A will rise in price, and a 60% chance that fund B will rise in price given that fund A rises in price. What is the probability that both fund A and fund B will rise in price?

0.36

Let P(A) =0.3 and P(B) = 0.4. Suppose A and B are independent. What is P(B I A)?

0.4

Patients scheduled to see their primary care physician at a particular hospital wait, on average, an additional eight minutes after their appointment is scheduled to start. Assume the time that patients wait is exponentially distributed. Refer to exhibit 6-3. What is the probability a randomly selected patient will see the doctor within five minutes of the scheduled time?

0.4647

Find the probability P(-1.96 < or equal to Z < or equal to 0)

0.4750

Gold miners in Alaska have found, on average, 12 ounces of gold per 1,000 tons of dirt excavated with a standard deviation of 3 ounces. Assume the amount of gold found per 1,000 tons of dirt is normally distributed. What is the probability the miners find more than 16 ounces of gold in the next 1,000 tons of dirt excavated?

0.4972

On a particular line, the likelihood that a light bulb is defective is 5%. Ten light bulbs are randomly selected. Refer to exhibit 5-7. What are the mean and variance of the number of defective bulbs?

0.50 and 0.475

The number of homes sold by a Realtor during a month has the following probability distribution: Number Sold Probability 0 0.20 1 0.40 2 0.40 Refer to exhibit 5-5. What is the probability that the Realtor sells no more than one house during a month?

0.60

The number of cars sold by a car salesman during each of the last 25 weeks is the following: Number Sold Frequency 0 10 1 10 2 5 Refer to exhibit 5-6. What is the probability that the salesman sells no more than one car during a week?

0.80

Consider the following probability distribution xi P(X = xi) 0 0.1 1 0.2 2 0.4 3 0.3 Refer to the exhibit 5-3. The standard deviation ______.

0.94

The foreclosure crisis has been particularly devastating in housing markets in much of the south and west United States, but even when analysis is restricted to relatively strong housing markets, the numbers are staggering. For example, in 2011 an average of three residential properties was auctioned off each weekday in the city of Boston, up from average of one per week in 2005. Rfer to exhibit 5-12. What is the probability that at least one foreclosure auction occurred in Boston on a randomly selected weekday of 2011?

0.9502

The waiting time at an elevator is uniformly distributed between 30 and 200 seconds. Find the mean and standard deviation of the waiting time.

115 seconds and 49.07 seconds

Let X be normally distributed with mean u = 250 and standard deviation o = 80. Find the value x such that P(X < or equal to x) = 0.0606

126

Let X be normally distributed with mean μ = 250 and standard deviation σ = 80. Find the value x such that P(X < or equal to x) = 0.0606.

126

A hedge fund returns on average 26% per year with a standard deviation of 12%. Using the empirical rule, approximate the probability the fund returns over 50% next year.

2.5%

The salaries of teachers in a particular school district are normally distributed with a mean of $50,000 and a standard deviation of $2,500. Due to budget limitations, it has been decided that the teachers who are in the top 2.5% of the salaries would not get a raise. What is the salary level that divides the teachers into one group that gets a raise and one that doesn't?

54,900

Which of the following is correct?

A continuous random variable has a probability density function, and a discrete random variable has a probability mass function.

Let X normally distributed with mean u and standard deviation o>0. Which of the following is true about the z value corresponding to a given x value?

All of the answers

Which of the following represents an empirical probability?

Based on past observation, a manager believes there is a 3-in-5 chance of retaining an employee for at least one year.

Let A and B be two independent events. If P(A) = 0.40 and P(B) = 0.20. Therefore,

P(AUB) =0.52

Which of the following can be represented by a continuous random variable?

The average temperature in Tampa, FL, during the month of July

What can be said about the expected value and standard deviation of an exponential distribution?

The expected value is equal to the standard deviation

Which of the following does not represent a continuous random variable?

The number of customer arrivals to a bank between 10 a.m and 11 a.m

What does it mean when we say that the tails of the normal curve are asymptotic to the x axis?

The tails get closer and closer to the x axis but never touch

A continuous random variable has the uniform distribution on the interval [a,b] if its probability density function f(x)

is constant for all x between a and b, and 0 otherwise

Find the z values such that P(Z < or equal to z) = 0.9082

z = 1.33

For an experiment in which a single die is rolled, the sample space is _____.

{2,1,3,6,5,4,}

Which of the following is not an event when considering the sample space of tossing two coins?

{HH, TT, HTH}

The intersection of events A = {apple pie, peach pie, pumpkin pie} and B = {cherry pie, blueberry pie, pumpkin pie} is

{pumpkin pie}