a human resource survey revealed that 30% of job applicants cheat on their psychometric test. use the binomial formula to find the probability that the number of job applicants in a sample of 14 who cheat on their psychometric test is:
a. exactly 8
b. less than 2
c. at least 1
In: Math
State Farm Insurance studies show that in Colorado, 45% of the auto insurance claims submitted for property damage were submitted by males under 25 years of age. Suppose 8 property damage claims involving automobiles are selected at random.
(b) What is the probability that six or more claims are made by
males under age 25? (Use 3 decimal places.)
(c) What is the expected number of claims made by males under age
25? What is the standard deviation of the r-probability
distribution? (Use 2 decimal places.)
| μ | |
| σ |
In: Statistics and Probability
Statistics is proving to be my nemesis!
According to Harper's Index, 55% of all federal inmates are serving time for drug dealing. A random sample of 15federal inmates is selected.
(a) What is the probability that 8or more are serving time for
drug dealing? (Round your answer to three decimal places.)
(b) What is the probability that 2or fewer are serving time for
drug dealing? (Round your answer to three decimal places.)
(c) What is the expected number of inmates serving time for drug
dealing? (Round your answer to one decimal place.)
In: Statistics and Probability
There are 3 car mechanics. They all fix a number of cars each year. Each mechanic (Mike, John, and Nick) have an rate for failing car parts. Find the probability that a car part fails. Hint. rate # of failed cars/ car work per person i.e. 2/40 for Mike.
| Mechanic | Portion of Car Work | # of failed cars |
|---|---|---|
| Mike | 40 | 2 |
| John | 10 | 3 |
| Nick | 50 | 4 |
Also, if the car part fails, find the probability that the car was produced by
A. Mike
B. John
C. Nick
In: Statistics and Probability
(a) Susan tries to exercise at ”Pure Fit” Gym each day
of the week, except on the weekends
(Saturdays and Sundays). Susan is able to exercise, on average, on
75% of the weekdays
(Monday to Friday).
i. Find the expected value and the standard deviation of the number
of days she
exercises in a given week. [2 marks]
ii. Given that Susan exercises on Monday, find the probability that
she will exercise at
least 3 days in the rest of the week. [3 marks]
iii. Find the probability that in a period of four weeks, Susan
exercises 3 or less days in
only two of the four weeks
In: Statistics and Probability
Suppose the sediment density (g/cm) of a randomly selected specimen from a certain region is normally distributed with mean 2.6 and standard deviation 0.78.
(a) If a random sample of 25 specimens is selected, what is the probability that the sample average sediment density is at most 3.00? Between 2.6 and 3.00? (Round your answers to four decimal places.) at most 3.00 between 2.6 and 3.00
(b) How large a sample size would be required to ensure that the probability in part (a) is at least 0.99? (Round your answer up to the nearest whole number.) specimens
In: Statistics and Probability
Each potential participant on a TV show like “Jeopardy” is given three tests of skill, T1, T2, T3 and receives a number on each test: 0 if Fail and 15 if Pass. The results on the three tests are averaged.
a. Describe the elements of a suitable sample space and the
random variable X which represents the potential participant’s
average score.
b. Find the probability mass function of X if the tests are
independent of each other and the probability of failing each test
is given by P(failing T1) = .8, P(failing T2) = .6, P(failing T3) =
.5.
In: Statistics and Probability
Suppose that the number of accidents occurring in an industrial plant is described by a Poisson distribution with an average of 1.5 accidents every three months. Find the probability that
In: Statistics and Probability
For a certain river, suppose the drought length Y is the number of consecutive time intervals in which the water supply remains below a critical value y0 (a deficit), preceded by and followed by periods in which the supply exceeds this critical value (a surplus). An article proposes a geometric distribution with p = 0.375 for this random variable. (Round your answers to three decimal places.)
(a) What is the probability that a drought lasts exactly 3 intervals? At most 3 intervals?
(b) What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?
In: Statistics and Probability
When commercial aircraft are inspected, wing cracks are reported as nonexistent, detectable, or critical. The history of a particular fleet indicates that 70% of the planes inspected have no wing cracks, 25% have detectable wing cracks, and 5% have critical wing cracks. Five planes are randomly selected.
(a) Find the probability that one has a critical crack, two have detectable cracks, and two have no cracks.
(b) Find the probability that at least one plane has critical cracks.
(c) Find the variance of number of planes having cracks (detectable and critical).
In: Statistics and Probability