Q1. In a game there are two spinners. The first spinner has the numbers 3, 1, 4 and the second spinner has the numbers 5, 6, 3, 2. Each spinner is spun once and the results are added. The probability that the sum is an even number is:
Q2. If a fair six-sided die is tossed twice, the probability that the first toss will be a number less than 4 and a second toss will be a number greater than 4 is:
Q3. A 5-digit PIN number can begin with any digit (except zero) and the remaining digits have no restrictions. If repeated digits are allowed, the probability of the PIN code beginning with a 7 and ending with an 8 is:
Q4. Seven people are randomly selected from a group of 10 men and 11 women to form a committee. The probability exactly 5 males are on the committee is:
Q5. A fair coin is tossed 14 times. What is the probability of obtaining exactly 1 head?
Q6. How many arrangements of the word ACTIVE are there if C and E must always be together?
Q7. A committee of 5 people is to be formed from a selection pool of 12 people. If Carmen must be on the committee, how many unique committees can be formed?
Q8. A tennis player has won 78% of her matches. The probability that she will win exactly 6 of her 9 matches is?
Q9. Given a standard normal curve, determine the approximate value of P(z > 1.12).
Q10. Test scores for a particular examination are normally distributed with a mean of 67.4% and a standard deviation of 10.5%. What is the probability of a student getting less than 80% on the test?
Q11. The marks on a mathematics exam were normally distributed with a mean of 64% and a standard deviation of 9%.
The marks on a economics exam were normally distributed with a mean of 64% and a standard deviation of 12%
If the distribution of the marks on the economics exam is put on the same axes as the distribution of the marks on the mathematics exam, then the curve would be
a. A different shape: taller and narrower
b. A different shape: shorter and wider
c. The same shape, shifted to the right
d. The same shape shifted to the left
Q12. Human body temperatures are normally distributed with a mean of 37.0 degrees and a standard deviation of 0.35 degrees. If a sample of 148 people is selected, determine the expected number of people in the sample with body temperatures above 37.5 degrees.
Q13. Weight loss from a particular diet are normally distributed with a standard deviation of 1.2kg. If 58% of the weight losses are 6.5kg or more, determine the mean weight loss, in kilograms.
Q14. A population of scores is normally distributed with a mean of 52.4 and a standard deviation of 14.3. If 40% of the scores are higher than the particular score x, calculate the value of x.
Q15. The shaded area under the standard normal curve shown is 0.33. Determine z.
Q16. Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.
Q17. The average number of typos on one page of a manuscript is 8. What is the probability that 4 to 6 typo appear on 2 pages of the manuscript? Assume Poisson distribution.
Q18. In a small town with two colleges, 1000 students were asked if they had an IPAD. The results of the survey are shown below:
|
|
Students with an IPAD
|
Students who do not have an IPAD
|
|
College A
|
365
|
156
|
|
College B
|
408
|
71
|
a. Find the probability that a randomly selected has an IPAD and is from College B, to the nearest hundredth.
b. Find the probability that a randomly selected students has an IPAD given that the student attends College B to the nearest hundredth.
Q19. In St. Lawrence College, 185 first year students were surveyed to determine which soil drinks they liked to drink, 115 drank coke, 92 drank root beer, 100 drank orange, 43 drank coke and orange, 52 drank root beer and coke, 57 drank root beer and orange, and 25 drank all three. Display this information In a Venn Diagram and answer the following questions.
How many students:
a. Drank only coke?
b. Drank coke or root beer?
c. Did not like to drink any of the three drinks?
Q20. Please upload a screen shot of your written work for the following question
The percentage of people who walk to work is 6.5%.
a. In a sample of 100 people what is the probability at least three of them walk to work?
b. How do you know this is a Binomial experiment?