Statistics and Probability Answers

the mean clotting time of blood is 7.45 seconds with a standard deviation of 3.6 seconds. what is the probability an individual's clotting time will be less than 3 seconds or greater than 11 seconds?

If my boss has 42 seats and 101 wheels, how many bikes and trikes does he have?

Three stores have 8, 12, and 15 employees of whom 3, 8, and 7, respectively, are women.

(i) A store is chosen at random and from that store an employee is chosen at random. If this employee is a woman, what is the probability she came from the store with 12 employees?

(ii) If a second employee is chosen from the same store in (i), what is the probability that a woman will be chosen? Assume that the employee chosen in (i) was a woman and we don’t know which store she came from.

[7 marks]

A group of chimpanzees are given two tasks to do, the second of which is harder than the first. A proportion 3/5 get the first one right and 7/15 get the second one right. If a chimpanzee gets the first one right, it has a conditional probability of 5/8 of also performing the second task right. One chimpanzee is chosen at random from the group.

(i) What is the probability that it gets both tasks right?
(ii) What is the probability that it gets at least one right?
(iii) If the chimpanzee got the first task wrong, what is the conditional probability that it will also get the second one wrong?
(iv) If the chimpanzee got the second task wrong, what is the probability that its first task was correctly carried out?
[12 marks]

Q3. An urn contains 7 balls, 4 of which are black and the rest white.
(a) Two are drawn together and one is found to be black. What is the probability that the other is also?
[5 marks]
(b) Starting with all 7 balls in the urn, balls are drawn randomly without replacement until all 3 white balls are found. What is the probability that the third white ball is found on the
(i) fourth attempt? (ii) seventh attempt?
[10 marks]

normal distribution, t distribution, x^2 distribution, F distribution, F test and X^2 test
1. standard distribution used when variable is known
2. family of distribution used for small sample sizes less than N=30
3. test used for ratio of variance of 2 normally distributed population
4. changes its non negative and asymetric shape depending on degree of freedom
5. has both numarator and denominator degree of freedom
6. test ysed for variance of normally distributed population.

please help with those definitions...its matching questions. So confuse. Thanks

A researcher hypothesized that the pulse rates of long-distance athletes differ from those of other athletes. He believed that the runners’ pulses would be slower. He obtained a random sample of 10 long-distance runners. He measured their resting pulses. Their pulses were 45, 45, 64, 50, 58, 49, 47, 55, 50, 52 beats per minute. The average resting pulse of athletes in the general population is normally distributed with a pulse rate of 60 beats per minute.

The mean number of major hurricanes to hit the USA per year is 0.6. Find the probability that
in a given year, more than one major hurricane will strike the USA.

A survey was conducted to measure the number of hours per week adults spend on home
computers. In the survey, the number of hours was normally distributed, with a mean of 8
hours and a standard deviation of 1 hour. A survey participant is randomly selected. Find the
probability that the hours spent on the home computer by the participant are between 5.5 and
9.5 hours per week.

An investment manager has all her bonds divided in three portfolios: P1, P2 and P3. The rst
portfolio (P1) collects the 20 percent of the bonds, the second (P2) 50 percent, and the third one (P3)
the remaining 30 percent. However, 5 percent of the bonds in the rst portfolio are defaulted, 2 percent
in the second are defaulted and, nally, the percentage of defaulted bonds in the third portfolio is 10
percent. If you buy one bond from the above manager, and it turns out to be defaulted, what is the
probability that it belongs to the rst portfolio P1? And what is the probability that belongs to any
of the other two portfolios (P2 and P3)?