Statistics and Probability Answers

A fitness center is interested in finding a 95% confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center. Records of 278 members were looked at and their mean number of visits per week was 2.1 and the standard deviation was 2.9. Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a Z or T distribution?

b. With 95% confidence the population mean number of visits per week is between ? and ? visits?

c. If many groups of 278 randomly selected members are studied, then a different confidence interval would be produced from each group. About (?) percent of these confidence intervals will contain the true population mean number of visits per week and about (?) percent will not contain the true population mean number of visits per week?

probability analysis and distribution about uses of internet for online studying and learning(450words)

bag of smokeless fuel are labeled as weighing 100kg but actual weights are normally distributed with a mean of 102kg and a standard deviation of 4kg.
What proportion of bag will weigh more than 106kg

. Find the area under the standard normal distribution which lies between Z = -0.45 and Z = 0.75?

Find the value of Z if the normal curve area between 0 and Z (positive) is 0.4332.

The mean expenditure per customer at a department store is Birr 85 with standard deviation of Birr 9. If a random sample of 40 customers is taken, what is the probability that the sample average expenditure per customer will be
a) Birr 87 or more
b) Less than Birr 82
c) Between Birr 83 and 85

Determine the value of c that makes the function f (x, y)= c(x + y) a joint probability density function over the range 0 < x < 3 and 0 < y < x. Determine the following:
a)P(X<1,Y<2)
b) P(1<x<2)
(c)P(Y>1) (e)E(X)
(d) P(X<2,Y<2)

(f) E(Y) (g) Marginal probability distribution of X

(h) Conditional probability distribution of Y given X = 1
(i) E (Y | X = 1) (j) P (Y > 2 | X = 1)
(k) Conditional probability distribution of X given Y = 2

A golfer recorded the following scores in 25 recent games:
88, 89, 102, 93, 99, 95, 94, 96, 84, 91, 95, 86, 95, 92, 102, 84, 104, 108, 92, 93, 92, 97, 96, 95, 82
a) Determine the mean and standard deviation
b) Assuming a normally distributed set of scores, what is the probability that the golfer will qualify for the club championship, which requires him to get a score under 83 on his next game?

Find the area under the standard normal distribution which lies between Z = -0.45 and Z = 0.75?

. Find the value of Z if the normal curve area between 0 and Z (positive) is 0.4332.