Statistics and Probability Answers

The batteries to the remote control for your television have just run out. you find your collection of miscellaneous "AA" batteries and grab 2 of them to replace the used ones. The box you used to fish out the replacements contained 14 batteries, but you were unaware that 5 of them were faulty and did not work.

if the remote control requires two good batteries to operate properly, what is the probability that the remote control now works properly?

What are the minimum, first quartile, median, third quartile, and maximum of the data set?

18, 20, 11, 10, 8, 6, 12, 4

Q. A box contains 10 red and 12 white rose flowers. Flowers are picked up at random one by one without replacement.
What is the probability that there are two red and three white flowers in the first five picked up?

It is noted that 8% of kaplan students are left handed if 20 (TWENTY) students are randomly selected, calculate the
i) probability that none of them are left-handed
ii) probability that at most 2 are left handed,
iii) standard deviation for the number of left-handed student

find the mean of the probability distribution of :number of sixes" in two tosses of unbiased dice ?

For every n>1 the random variable Xn is exponential with parameter λn, where λn→λ>0 an X is an exponential with parameter λ, then show that Xn converges in distribution to X

Construct a 95% confidence interval for the population mean of hourly wage. What sample size would you need if you wanted the confidence interval to have a width of at most $1 on either side of the sample mean (so $2 in total)?

Population mean: 5.185577655

Hourly wage:
1.878125
2.0125
2.058333
2.510417
2.752404
2.754464
3.007813
3.127404
3.188101
3.360902
3.367789
3.800481
3.822917
3.848558
3.851923
4.165865
4.357778
4.810096
5.071875
5.164063
5.5025
5.771635
5.771635
5.8675
5.985043
7.503125
8.079327
12.5025
12.65825
15.62891

6 Suppose a fair on is tossed three times, what is the probability that at least one head occurs?

7 Suppose a box contains 4 red balls and 3 black balls. Compute the probability that the second ball drawn is red if the first ball drawn was black.

8 There are three children in a family. If there is at least one boy and at most two boys in this family. What is the conditional probability that there are exactly two boys in this family?

9 Two women A, and B share an office with a single telephone. The probability that any call will be for A is 2/3 . Suppose that A is out of her office during the office hours half of the time and B one third. Find the probability that for any call during the working hours. A call can be answered by the person being called.

10 A box contains 6 balls numbered 1 to 6. A ball was drawn from the box at random. Find the probability that the number on the ball drawn was either 1, 2, or 6

1 In how many ways can a family of 9 divide itself into 3 groups so that each group contains 3 persons?

2 Four digits numbers are to be formed using any of the digits 1, 2, 3, 4, 5, 6. If no repetition of digit is allowed how many 4-digit even numbers can be formed?

3 A club consist of 10 men and 5 women, in how many ways can a committee of 6 consisting of 4 men and 2 women be chosen?

4 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.

5 Let A and B be any two events defined on the same sample spaceSuppose P(A) = 0.3 and P(A B) = 0.6. Find P(B) such that A and B are mutually exclusive.

6. In how many ways can a committee of 3 people be chosen out of 8 people?
7 A coin is rolled thrice, what is the event that two heads occur?.
8 What is the number of possible outcomes assumed to be equally likely if a coin is tossed thrice?.
9 Write down the sample space for a box containing 6 items of which 2 are defective. One item is chosen one after the other without replacement until the last defective item is chosen.
10 In how many ways can 12 objects be split into three groups containing 2,4 and 6 objects?