Chapter 4
Amy has tulips, daffodils, and marigolds in her garden. If she is conducting a random sample of the flowers what is the sample space?
{Tulips, Daffodils, Marigolds}
To get the likelihood that exactly x observations do the action which we are examining, we use what calculator function?
Binompdf
To find the area under the curve between -1.4 and 0.69 you use what calculator function?
In what sequence are the values entered?
Normalcdf
Lower bound, upper bound, mean standard deviation.
A new car is being released by company A. They are testing to see if their gas mileage claims are accurate, so they take a SRS of 15 new cars and measure the gas mileage. Assume the sample is normally distributed. From this sample, they have a mean of 37.7 mpg and a standard deviation of 4.22 mpg. What is the margin of error for this problem at the following levels:
a. 90% confidence
b. 95%
c. 99%
a. 1.92
b. 2.34
c. 3.24
Acme produces thousands of GetRoadrunner Gadgets each day. The probability of an item being defective from the Acme production line is 8%.
a. What is the probability that if two items are randomly selected from the production line, both will be defective?
b. What about if five items are selected?
a. 0.0064
b. 0.00000328
View the probability distribution below and answer the following questions:
x: 3 5 7 9 11 13
P(x): .12 .28 .23 ??? .12 .06
What is the probability of getting exactly 9 occurrences?
0.19
If we know the area underneath the curve, but need the cut off values, what calculator function do we use?
Inverse Norm.
A psychologist has developed a new test for spatial perception. And she wants to estimate the mean
score achieved by male pilots. How many people must she test if she wants a margin of error of 2 points
with 95% confidence? Assume σ= 21.2
432 pilots.
A sports shop has a bin with different colored golf balls in it. The bin has 110 white balls, 50 pink balls, 30 yellow balls, and 6 purple balls.
a. What is the probability that if you reach into the bin without looking you will get a pink ball?
b. Would it be unusual to get a purple ball? Justify your answer.
a. 0.2551
b. Yes it would be unusual because the probability of getting a purple ball is less than 0.05 (P(p) = 0.0306)
Jay is a salesman who has kept up with his computer sales over the last year. Let X = the number of computers sold in a day. The following represents the probability distribution for X:
x: 0 1 2 3 4
P(x): 0.2 0.1 0.3 0.2 0.2
a. Verify this is a legitimate probability distribution.
b. What is the probability that Jay will sell 3 computers in a given day?
c. What is the probability that Jay will sell either 1 or 2 computers in a given day?
a. It is legitimate because all probabilities add to 1 and are between 0 and 1.
b. 0.2
c. 0.4
How many types of problems do we use with Normcdf and what are they?
3. Population standard deviation problems, sample standard deviation problems, and proportion problems.
In a SRS of 7028 male high school students, it was found that 1926 of them played video or computer
games for 3 or more hours per day. Find a 95% confidence interval for the proportion of high school
students who play video games 3 or more hours a day
(0.2636,0.2845)
Employees of a small company were asked about their transportation to work. Of the 20 employees, 3 walk to work, 5 use public transportation, and the remaining employees drive their own car.
a. What is the sample space?
b. Create a probability model for this question.
c. What is the probability that an employee selected at random drives to work?
d. What is the probability that an employee does not walk to work?
a. {walk, public transport, drive}
b. Administrators Discretion
c. 0.6
d. 0.85
It is reported that 4% of American teens and adults have a food allergy. Assume we take a sample of 12 American teens and adults. Calculate the probability for the following:
a. What is the probability that exactly 3 of them have a food allergy?
b. What is the probability that exactly 8 of them have a food allergy?
a. 0.0098
b. 0.0000000028
Assume we are told that 23% of the Freshmen admitted to KSU were classified as non-traditional students. If I take a random sample 150 freshmen,
a. What is the probability that more than 30% of the sample are non-traditional students?
b. What is the probability that between 18% and 21% are non-traditional students?
a. 0.0208
b. 0.2074
A test is made of H0: mu = 40 verses H1: mu > 40. A sample of size 26 is drawn. The sample mean and standard deviation are 46 and 10, respectively.
0.0026. 25. Yes. No.
Refer to the table on slides to answer the following questions:
a. What is the probability that Julie will pick a romance book out of the box?
b. What is the probability that Julie will pick a book she has not read given that it’s a mystery novel?
c. What is the probability that Julie will pick a fantasy book or one that she has read?
a. 0.375
b. 0.3
c. 0.75
A local artist is considering the purchase of a new storefront to increase business. Let X be the random variable representing the number of customers to be gained in a month based on data from a studio with a similar size and demographic.
X 4 6 8 10 12 14 16
P(X) 0.15 0.2 0.34 0.19 0.06 0.05 0.01
a. What is the probability that at least 6 customers’ business will be gained from the venture?
b. What is the probability that no more than 10 customers will be gained from the venture?
a. 0.85
b. 0.88
The scores on a nation-wide achievement test are Normally distributed with a mean of 320 and a standard deviation of 78.
a. What is the probability that the score for a randomly selected student is less than 318?
b. What is the score that marks the cut-off for the top 25%? c. What is the probability that a sample of 50 students is between 300 and 315?
a. 0.4898
b. 372.61
c. 0.2903
A poll taken by the software usability research laboratory surveyed 341 video gamers, and 110 of them said that they prefer playing games on a console, rather than on a computer or handheld device. An executive at a game console manufacturing company claims that more than 25% of gamers prefer consoles. Does the poll provide convincing evidence that the claim is true? Use an alpha level of 0.01 in testing your hypothesis.
(Reject H0). Yes, it provides enough evidence to suggest that the claim is true.