1
What is the probability of an event that is certain to happen?
What is 1?
A person has a 7% chance of winning the daily office lottery. What is the probability she first wins on the 3rd day?
What is (0.07)(0.93)^2
A manufacturer knows that 15% of the widgets coming off the assembly line have a minor defect. If and inspector keeps inspecting units until he comes upon one with the defect, what is the probability he will have to inspect at most 4 widgets?
Workout
0.15 + (0.85)(0.15)+(0.85)^2(0.15)+(0.85)^3(0.15)
Suppose X and Y are random variables with ux=45, sdx=12, uy=42 and sdy= 5. Given that X and Y are independent, what is the standard deviation of the random variable X-Y?
What is 13?
Workout
12^2 + 5^2= 169 square root it because variances add.
6.7% of women graduate college with STEM degrees. In a SRS of 1000 women, what is the probability that more than 8% will graduate college with a STEM degree?
What is 0.05?
workout
1-biomcdf(1000,0.067,80) or normalcdf
If the probability of rain is 0.35, what is the probability that it does not rain?
What is 0.65?
According to a college's records, 46% of its students live in the dorms, 65 percent have meal contracts and 33% do both. For a randomly selected student, what is the probability that he/she either lives in a dorm or has a meal contract, but not both?
What is 0.45?
P(Not meal but dorm)=0.46-0.33=0.13
P(Not dorm but meal)=0.65-0.33=0.32
In a set of 10 boxes, 7 boxes each contain 3 red and 2 blue marbles, while the remaining boxes each contain 1 red and 4 blue marbles. A player randomly picks a box and then randomly picks a marble from that box. She wins if she ends up with a red marble. If she plays 4 times, what is the probability she wins exactly twice?
What is 6{0.48}^2 x {0.52}^2
Which of the following are unbiased estimators for the corresponding population parameters?
I Sample means. II Sample proportions
III Difference in sample means. IV Difference of sample proportions
What is All are unbiased?
The variance of a set of data is 5. If every value in the set is multiplied by 4 and then added to 100, what is the new variance?
What is 80?
Workout
4^2 x 5
If P(A)=0.4, P(B)=0.5 and
P(A upside down U B)=0.2, find P(A U B)
What is 0.7?
2 fair coins are tossed. If both land on heads, the player wins $5. If exactly 1 lands on heads, the player wins $2. If it costs $3 to play, what is the player's expected outcome after six games?
What is Loss of $4.50?
Workout
5(0.25)+2(0.5)-3=-0.75 For 6 games the EC is 6(-0.75)
What is 1/3 ?
Body temperatures of healthy humans are roughly normal. If 10% of people have temperatures above 37.333 degrees Celcius and if 20% have temperatures below 36.781 degrees Celcius, What is the mean of this distribution?
What is 37.000 degrees Celcius?
Hint
InvNorm
If the power of a test is 0.85, what is the probability of a Type II error?
What is 0.15?
A fair coin is flipped 8 times. What is the probability of getting at least one head?
What is 1-(1/2)^8=255/256
85% of people wear seat belts. The probability of serious injury in an accident is 8% for those wearing seat belts and 36% for those not wearing seatbelts. What is the probability of serious injury in an accident?
What is 0.122?
What is the complement of "at least one"?
What is none?
In a geometric distribution, what does X represent?
What is the trial number of first success?
If X~N(100,15), what is the z-score for 130?
What is 2?
Approximately what percent of observations lie within 2 standard deviations of the mean?
What is 95%
Suppose 2 events, S and T, have the nonezero probabilities p and q, respectively. Which of the following is impossible?
What is S and T are both independent and mutually exclusive?
A college library determines that books are checked out for and avg. of 8 days with an SD of 2 days. Assuming a roughly normal distribution, what is the shortest time interval for which two thirds of the books are out?
What is 6.1 to 9.9 days?
Hint
Empirical rule on graph
Suppose that the avg. age of MLB players is 26.8 with a SD of 3.8, while the avg. age of NFL players is 25.6 with a SD of 2.9. In random samples of 35 MLB players and 30 NFL players, what is the probability that the mean age of MLB players is greater than the mean age of the NFL players?
What is 0.9253?
Workout
uMLB-uNFL=26.8-25.6=1.2
(sd)MLB-sd(NFL)= square root 3.8^2/35+2.9^2/30=0.8324
P(Xbar--MLB-NFL >0)=P(z>0-1.2/0.324)
You win a game if you toss a faire die with 5 coming up in exactly 1/6 of the tosses. Would you rather flip 12 times or 120 times?
What is 12 times because 0.296>0.0973?
Hint
Law of large numbers also use Binompdf