Download Portage Learning MATH 110 All Exams statistics questions with complete answers LATEST test and more Exams Nursing in PDF only on Docsity!
Mod 1 Exam 1
- Define each of the following: a) Observation b) Element c) Variable
Observation- all the information collected for each element in a study
Element- in a data set, the individual and unique entry about which data has been collected, analyzed and presented in the same manner Variable- a particular, measurable attribute that the researcher believes is needed to describe the element in their study.
- Explain outliers
An outlier is a value which is out of place compared to the other values. It may be too large or too small compared to the other values
- Look at the following data and see if you can identify any outliers: 53 786 789 821 794 805 63 777 814 2333 783 811 795 788 780
Outliers: 53 63 2333
a) How many were burgers? b) How many were fish?
- a) Burgers, 2900(0.12)=
- b) Fish, 2900(0.28)=
b.
- Suppose that you have a set of data that has a mean of 49 and a standard deviation of 8. a) Is the point 57 above, below, or the same as the mean. How many standard deviations is 57 from the mean. b) Is the point 33 above, below, or the same as the mean. How many standard deviations is 33 from the mean. c) Is the point 31 above, below, or the same as the mean. How many standard deviations is 31 from the mean. d) Is the point 79 above, below, or the same as the mean. How many standard deviations is 79 from the mean. a) The data point 57 is above the mean. Now use the z-score to determine how many standard deviations 57 is above the mean. We are told that the mean is 49 and the standard deviation is 8. So, the z-score is given by:
The z-score is 1, so the data point 57 is 1 standard deviation above the mean.
b) The data point 33 is below the mean. Now use the z-score to determine how many standard deviations 33 is below the mean. We are told that the mean is 49 and the standard deviation is 8. So, the z-score is given by:
The z-score is -2, so the data point 33 is 2 standard deviations below the mean (the negative sign indicates that the point is below the mean).
c) The data point 31 is below the mean. Now use the z-score to determine how many standard deviations 31 is below the mean. We are told that the mean is 49 and the standard deviation is 8. So, the z-score is given by:
The z-score is -2.25, so the data point 31 is 2.25 standard deviations below the mean (the negative sign indicates that the point is below the mean).
d) The data point 79 is above the mean. Now use the z-score to determine how many standard deviations 79 is above the mean. We are told that the mean is 49 and the standard deviation is 8. So, the z-score is given by:
The z-score is 3.75, so the data point 79 is 3.75 standard deviations above the mean.
- Consider the following set of data: {20, 5, 12, 29, 18, 21, 10, 15}
a) Find the median. b) Find the mode of this set. a) In order to find the median, we must first put the numbers in ascending order:5,
10, 12, 15, 18, 20, 21, 29.
Notice that there are two “middle” numbers, 15 and 18. The median is the average of these two numbers. Median = (15+18)/2 = 16.5.
b) No number occurs more than once, so there is “no mode”.
Exam 3
- Find the answer to each of the following by first reducing the fractions as much as
possible:a) P(412,3)=
b) C(587,585)=
- Suppose you are going to make a password that consists of 5 characters chosen from {1,2,4,9,d,i,k,m,n,w,z}.How many different passwords can you make if you cannot use any character more than once in each password?
- Suppose A and B are two events with probabilities:
P(A)=.35, P(Bc^ )=.45, P(A∩B)=.25.
Find the following:
a) P(A𝖴B). b) P(Ac^ ). c) P(B). a. For P(A 𝖴 B). Use P(A 𝖴 B)=P(A)+P(B)-P(A∩B). But for this equation, we need P(B) which we can findby using P(B)=1-P(Bc^ ). So, P(B)=1-.45= .55.
P(A𝖴B)=.35+.55-.25=.
b. For P(Ac^ ). Use P(A)=1-P(Ac^ ) which may be rearranged to (Ac^ )=1-P(A).
P(Ac^ )=1-.35=.65.
c. For P(B). Use (B)=1-P(Bc^ ).
P(B)=1-.45=.55.
- Suppose A and B are two events with
probabilities:P(Ac^ )=.50, P(B)=.65,
P(A∩B)=.30.
a) What is (A│B)? b) What is (B│A)?
- In a manufacturing plant, three machines A, B, and C produce 30 %, 20 %, and 50 %, respectively, of the total parts production. The company's quality control department determined that 3 % of the parts produced bymachine A, 2.5 % of the parts produced by machine B, and 4 % of the parts produced by machine C are defective. If a part is selected at random and found to be defective, what is the probability that it was producedby machine B?
- The probability that a certain type of battery in a smoke alarm will last 3 years or more is .85. The probability that a battery will last 7 years or more is .25. Suppose that the battery is 3 years old and is stillworking, what is the probability that the battery will last at least 7 years?
- Suppose that 7 out of 17 people are to be chosen to go on a mission trip. In how many ways can these 7 be chosen if the order in which they are chosen is not important.
Exam 4
- In a large shipment of clocks, it has been discovered that 21 % of the clocks are defective. Suppose that you choose 7 clocks at random. What is the probability that 2 or less of the clocks are defective.
- Find each of the following probabilities: (use standard normal distribution table to get z-score) a. Find P(Z ≤ 1.27). b. Find P(Z ≥ -.73). c. Find P(-.09 ≤ Z ≤ .86).
a. P(Z ≤ 1.27) =0.
b.P(Z ≥ -0.73= 1- P(Z ≤ -0.73)=1- 0.23270=0.
c. P(-0.09 ≤ Z ≤0 .86)= P(Z≤0 .86)- P(Z≤ -0.09)
0.80511-0.46414=.
- A company manufactures a large number of rods. The lengths of the rods are normally distributed with a mean length of 4.0 inches and a standard deviation of .75 inches. If you choose a rod at random, what is theprobability that the rod you chose will be: a) Less than 3.0 inches?
b) Greater than 3.7 inches? c) Between 3.5 inches and 4.3 inches?
- An archer is shooting arrows at a target. She hits the target 68% of the time. If she takes 15 shots at thetarget, what is the probability that she will hit the target exactly 12 times?
Exam 5
- Suppose that you take a sample of size 20 from a population that is not normally distributed. Can thesampling distribution of x̄ be approximated by a normal probability distribution?
No because the sample has to be at least 30 to use sampling distribution of x̄ or be normally distributed.
- Suppose that you are attempting to estimate the annual income of 2000 families. In order to use the infinitestandard deviation formula, what sample size, n, should you use?
Your Answer:
n N ≤ 0.
n 2000 ≤ 0.
n ≤ 0.05(2000)=
Sample size must be less than 100
- Suppose that in a large hospital system, that the average (mean) time that it takes for a nurse to take the temperature and blood pressure of a patient is 150 seconds with a standard deviation of 35 seconds. What is the probability that 30 nurses selected at random will have a mean time of 155 seconds or less to take the temperature and blood pressure of a patient?
We calculate the standard deviation of the sample distribution:
