Some statistics students estimated that the amount of change daytime statistics

Question

Some statistics students estimated that the amount of change daytime statistics students carry is exponentially distributed with a mean of $0.88. Suppose that we randomly pick 25 daytime statistics students.

Part (a)

In words, define the random variable X.

Correct! The variable of interest is the amount of change that a daytime statistics student carries.

Part (b)

Give the distribution of X.
X ~ exp

Part (c)

In words, define the random variable

X.

Correct! This represents the average of the random variable, amount of change.

Part (d)

Give the distribution of

X.

(Round your standard deviation to three decimal places.)

X

~

   ,

Part (e)

Find the probability that an individual had between $0.71 and $0.90. (Round your answer to four decimal places.)


Graph the situation, and shade in the area to be determined.

Part (f)

Find the probability that the average of the 25 students was between $0.71 and $0.90. (Round your answer to four decimal places.)


Graph the situation, and shade in the area to be determined.

Part (g)

Explain why there is a difference between parts (e) and (f).

a. The graph of the amount of change becomes more normal as the sample increases; therefore, in part (e), the graph is approximately normal and in part (f), the graph is exponential.

b. The graph of sample means becomes more normal as the sample increases; therefore, in part (f), the graph is approximately normal and in part (e), the graph is exponential.    

c. There is always a better chance for 25 people to have between $0.71 and $0.90 than for 1 person to have that amount.

d. There is always a better chance for one person to have between $0.71 and $0.90 than for 25 people to each have that amount.

I'm lost! On part b it is looking for exponents but when i do it I don't get the correct answer x~exp ( ) because i asked the instructor....

Explanation / Answer

Hope you are looking for the answer to part b. The correct answer for that would be X ~ exp (0.88).

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