Chapter 4
An experiment has four steps with 2 possible outcomes for the first step, 3 possible outcomes for the second step, 6 possible outcomes for the third step, and 3 possible outcomes for the fourth step. How many experimental outcomes exist for the entire experiment?
108 possible outcomes
0.2
What is a standard normal probability distribution?
A normal distribution with a mean of zero and a standard deviation of one
What does the 68, 95, 99.7 rule mean?
68 percent of the data lays within one standard deviation of the mean, two standard deviations is 95 percent of the data, and three standard deviations is 99.7 percent of the data.
Scores on a particular test are normally distributed with a standard deviation of 4 and a mean of 30. What is the probability of anyone scoring less than 40?
.9938
A gym tracks the number of calls they get per week. Use Table 1 on the Google Doc to find the probability that a call will be going to the Aquatics Department? (to four decimal places)
0.2966
If a coin is tossed 5 times, using binomial distribution find the probability of:
(a)Exactly 2 heads
(b) At least 4 heads.
(a) 5/16
(b) 3/16
The area in a uniform probability distribution should be equal to what?
1
Most graduate schools of business require applicants for admission to take the Graduate Management Admission Council’s GMAT examination. Scores on the GMAT are roughly normally distributed with a mean of 527 and a standard deviation of 112. What is the probability of an individual scoring above 500 on the GMAT?
0.5948
IQ scores have a normal distribution with a mean of 100 and a standard deviation of 15. What percent of people have an IQ above 120?
9.18%
Using Table 2 on the Google Doc, what is the probability that someone who wants kids doesn't like kids? (to four decimals)
.0762
If X is binomially distributed with 6 trials and a probability of success equal to (1/4) at each attempt, what is the probability of exactly 4 successes?
0.033
The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years. If you drew a uniform probability distribution, what would the hight of your rectangle be?
1/9
. Most graduate schools of business require applicants for admission to take the Graduate Management Admission Council’s GMAT examination. Scores on the GMAT are roughly normally distributed with a mean of 527 and a standard deviation of 112. How high must an individual score on the GMAT in order to score in the highest 5%?
711.24
Annual salaries for a large company are approximately normally distributed with a mean of $50,000 and a of $20,000. What percentage of company workers may under $40,000?
30.85%
You toss a coin three times, what is the probability that you toss exactly three heads?
1/8
If electricity power failures occur according to a Poisson distribution with an average of 3 failures every twenty weeks, calculate the probability that there will not be more than one failure during a particular week.
0.98981
The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years. What is the expected age of a given car?
5 years old
The Edwards’s Theater chain has studied its movie customers to determine how much money they spend on concessions. The study revealed that the spending distribution is approximately normally distributed with a mean of $4.11 and a standard deviation of $1.37. What percentage of customers will spend less than $3.00 on concessions?
20.9%
If you are two standard deviation away from the mean in both directions, what percent of the data are you covering?
95% of the data
In Lila's hometown it's rainy one third of the days. Given that it is rainy, there will be heavy traffic with probability 1212, and given that it is not rainy, there will be heavy traffic with probability 1414. If it's rainy and there is heavy traffic, she arrive late for work with probability 1212. On the other hand, the probability of being late is reduced to 1818 if it is not rainy and there is no heavy traffic. In other situations (rainy and no traffic, not rainy and traffic) the probability of being late is 0.250.25. You pick a random day. What is the probability that she is late?
1/12+1/24+1/24+1/16
=11/48.
Suppose N=20 and r=9.
What is the probability that n=7 and x=4? (to four decimal places)
0.2682
The amount of candy dispensed by a candy machine is normally distributed with a mean of 0.9 oz and a standard deviation of 0.1 ounces. If the machine is used 500 times, how many times will it dispense more than 1 oz of candy?
79.35
The Edwards’s Theater chain has studied its movie customers to determine how much money they spend on concessions. The study revealed that the spending distribution is approximately normally distributed with a mean of $4.11 and a standard deviation of $1.37. What spending amount corresponds to the top 87th percentile?
$2.56
The amount of time a student taking statistics spends on studying for a test is normally distributed. If the average time spent studying is 12 hours and the standard deviation is 4 hours, what is the probability that a student will spend more than 8 hours studying?
84.13%