Statistics and Probability Answers

1 If a coin is tossed three times and the total number of tails are observed, what is the sample space for the experiment?.

2 Relative frequency approach is the same as……..

3 A bag contains 2 natural oranges and 3 artificial oranges. Each of four persons, A, B, C, and D, in the order named, draws one orange and does not replace it. The first to draw a natural orange receives N20. What is the probability that A, B, and C lose and D wins

4 If a die is thrown once, what is the probability of getting an even number?.

5. 4 different Biology books, 6 different CIT books and 2 different Mathematics books are to be arranged on a shelf. How many different arrangements are possible if only the Biology books must stand together?

8 Let X have a uniform distribution on the interval [A,B]. compute V(X)

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

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

3 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

Let X be a continuous rv with cdf
F(x)=⎧⎩⎨⎪⎪0x4[1+ln(4x)]0x≤05≤y≤10x>4
F(x)={0x≤0x4[1+ln(4x)]5≤y≤100x>4
. What is the pdf of X?
7 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?

2 Components of a certain type are shipped to a supplier in batches of ten. Suppose that 50% of all such batches contain no defective components. 30% contain one defective component, and 20% contain two defective components. Two components from a batch are randomly selected and tested. What are the probabilities associated with 0.1, and 2 defective components being in the batch under the condition that neither tested component is defective.

4 The error involved in making a certain measurement is a continuous rv X with pdf
f(x)={0.09375(4−x2)0−2≤x≤2otherwise
f(x)={0.09375(4−x2)−2≤x≤20otherwise
compute P(-1

1 A certain shop repairs both audio and video components. Let A denote the event that the next component brought in for repair is an audio component, and let B be the event that the next component is a compact disc player (so the event B is contained in A). Suppose that P(A)= 0.6 and P(B) =0.05. What is P(P|A)

Q. A marble is drawn at random from a box containing 10 red, 30 white, 20 blue and 15 orange marbles. Find probability that it is
(i) Orange or red
(ii) Not red or blue
(iii) Not blue
(iv) Red, white or blue

Q. Find the probability for each of the following events:
(i) An odd number appears in a single toss of a fair die
(ii) The sum appears in a single toss of a pair of fair dice.
(iii) At least one head appears in three tosses of a fair coin.
(iv) A king, ace, jack of clubs or queen of diamonds appear in drawing a single card from a well shuffled ordinary deck of 52 cards.

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
(i) First 3 flowers are red
(ii) There are 2 red and 3 white flowers
In the first four picked up.
(iii) The third one is red given that the first 2 are white

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

1) A survey was conducted to measure the number of hours per week adults spend on home computers. In the survey, the number of hours were normally distributed, with a mean of 7 hours and a standard deviation of 1.5 hours.

a) What is the probability that the sample mean of 9 participants exceeds 8 hours?

b) What is the probability that the sample mean of 9 participants is below 6.5 hours?


c) What is the probability that the sample mean of 25 participants is between 6.8 and 7.8 hours?