Statistics and Probability Answers

Let A and B be any two events defined on the same sample space. Suppose P(A) = 0.3 and P(A B) = 0.6. Find P(B) such that A and B are independent.

1.The set of data a={ 12,6,7,3,15,10,18,5 } and b={ 9,3,8,8,9,8,9,18 }.
i. Measure the central tendency(mean, median, mode ,GM,HM) of a given data set and explain which one is the poor measure
ii. Measure the dispersion(range, mean deviation, standard deviation, variance) of a given data set and explain which one is the poor measure
iii. Measure the skewness and kurtosis of a given dataset and explain

A metal sheet has, on the average, 5 defects per 1.0 m2
. Assuming a Poisson
distribution, calculate the probability that a 1.5 m2
piece of the metal sheet will have
at least 4 defects.

Out of 90 applicants for a job, 60 people get selected after the interview. If five
applicants are selected at random, calculate the probability that 2 will get selected.

An unbiased coin is tossed three times. If A is the event that a head appears on each
of the first two tosses, B is the event that a tail occurs on the third toss and C is the
event that exactly two tails appear in the three tosses, show that:
i) Events A and B are independent
ii) Events B and C are dependent.

According to the US Census Bureau, 7.1% of Americans living in 2010 were between the
ages of 20 and 24. Suppose that a random sample of 50 Americans taken this year found
6 between the ages of 20 and 24. If appropriate, test whether the population proportion
has increased since 2010, using level of significance

At a party, you and your friend are both eying the last slice of pizza. To settle the matter, you agree on the following dice game: each of you is going to roll a die; if the highest number rolled by either one of you is a 1, 2, 3 or 4, then Player 1 wins. If the highest number is a 5 or a 6, then Player 2 wins. Assuming that you really want that last slice of pizza would you rather be Player 1 or Player 2 to maximize your chance of winning? Explain your choice.

Let X have a standard gamma distribution with
α=7
. Compute P(X<4 or X>6)
0.912
0.625
0.812
0.713

10 Let X = the time between two successive arrivals at the drive –up window of a bank. If X has a exponential distribution with h=1 ( which is identical to a standard gamma distribution with a=1). Compute the standard deviation of the time between successive arrivals
2
1
3
4

In a study of plants, five characteristics are to be examined. If there are six recognizable differences in each of four characteristics and eight, recognizable difference in the remaining characteristics. How many plants can be distinguished by these five characteristics?
120
150
80
70

8 Let X have a uniform distribution on the interval [A,B]. compute V(X)
B−A12−−√
A−B2√
B+A12−−√
BxA2√

Each of 12 refrigerators of a certain type has been returned to a distributor because of an audible, high-pitched, oscillating noise when the refrigerator is running. Suppose that 7 of these refrigerator have defective compressor and the other 5 have less serious problems. If the refrigerators are examined in random order. Let X be the number among the first 6 examined that have a defective compressor. What is the probability that X exceeds its mean value by more than 1 standard deviation
0.132
0.121
0.112
0.651

4 The error involved in making a certain measurement is a continuous rv X with pdf
f(x)={0.09375(4−x2),−2≤x≤2
0,otherwise
compute P(-1<X
0.6875
0.3425
0.3662
0.5522