Question

Some statistics students estimated that the amount of change daytime statistics students carry is exponentially distributed with a mean of $0.72. Suppose that we randomly pick 25 daytime statistics students.

a) Give the distribution of X.

b) Give the distribution of X. (Round your standard deviation to three decimal places.)

c) Find the probability that an individual had between $0.67 and $0.95. (Round your answer to four decimal places.)

d) Find the probability that the average of the 25 students was between $0.67 and $0.95. (Round your answer to four decimal places.)

Answer 1

a) distribution of X is exponential with parameter =0.72

b) distribution of Xbar follows approximately normal distribution with parameter mean =0.72 and std deviation x=0.72/sqrt(25)=0.144

c)

P(0.67<X<0.95)=P(X<0.95)-P(X<0.67)=(1-e^-0.95/0.72)-(1-e^-0.67/0.72)=0.1271

d)

P(0.67<Xbar<0.95)=P((0.67-0.72)/0.144<Z<(0.95-0.72)/0.144)=P(-0.35<Z<1.60)=0.9452-0.3632=0.5820