Statistics and Probability Answers

1.      Current estimates suggest that 72% of the home-based computers in a country have access to on-line services. Suppose 16 people with home-based computers were randomly and independently sampled. Find the probability that fewer than 9 of those sampled currently have access to on-line services. Show your work. (3)

Answer =  

2.      Given that X is a normally distributed variable with a mean of 52.2 and a standard deviation of 2.3, find the probability that X is between 47 and 54. (1)

Answer=

3.      A machine fills jars with coffee beans. The weight of the beans that the machine puts in a jar follows a normal distribution with the mean 246 grams and the standard deviation 3.5 grams. The label on a jar says, “weight 240 grams.” Two filled jars are selected at random. Find the probability that at least one of them is under-filled (has less than 240 grams of beans in it). Show your work. (4)

drawing one card from a deck and then another card. is it a dependent or indepedent event?

Based on the previous data, the probabilities of a batsman making various scores in a tournament are as :

Runs Probability

10 0.01

20 0.20

30 0.15

50 0.30

60 0.12

70 0 20

100 0.02

To simulate the runs scored by the batsman in the next five tournaments using the following choice of random numbers : 25, 39, 65, 76, 12.

. Random sample of size 4 are drawn from the finite population which consists of the numbers 2,3,7,8,and 10.

a. What is the population mean, population variance and population standard deviation of the given data?

b. What is the sampling distribution of the sample means for a sample of size 2 which can be drawn without replacement from the given population?

c. What is the mean, variance and standard deviation of the sampling distribution?

A nutrition teacher wants to compare the food values of the nutrition and dietetics students with those of the engineering students. She constructed a questionnaire composed of 15 items. The teacher administered the questionnaire to engineering and nutrition students. What conclusion can the nutrition teacher draw about the food value of the students? 

1.     Suppose that U is a random variable giving the number of tails minus the number of heads in three (3) tosses of a coin. List the elements of the sample space S for three (3) tosses of the coin and to each sample point assign a value u of U. 

What sample size should be obtained to determine a 94% confidence within 4%?

class of 30 of these pupils is used as sample. what is the probability that the class mean is greater than 46 inches

Two thousand tickets are sold  each. One ticket will win , two tickets will win  each and three tickets will win  each. Let  denotes the net gain from the purchase of a randomly selected ticket

What is probability?