49.

*Χ*= amount of change students carry*Χ*~*E*(0.88, 0.88)- $\stackrel{\u2013}{X}$ = average amount of change carried by a sample of 25 students.
- $\stackrel{\u2013}{X}$ ~
*N*(0.88, 0.176) - 0.0819
- 0.1882
- The distributions are different. Part a is exponential and part b is normal.

51.

- length of time for an individual to complete IRS form 1040, in hours.
- mean length of time for a sample of 36 taxpayers to complete IRS form 1040, in hours.
*N*$\left(\text{10}\text{.53,}\frac{1}{3}\right)$- Yes. I would be surprised, because the probability is almost 0.
- No. I would not be totally surprised because the probability is 0.2312

53.

- the length of a song, in minutes, in the collection
*U*(2, 3.5)- the average length, in minutes, of the songs from a sample of five albums from the collection
*N*(2.75, 0.066)- 2.74 minutes
- 0.03 minutes

55.

- True. The mean of a sampling distribution of the means is approximately the mean of the data distribution.
- True. According to the Central Limit Theorem, the larger the sample, the closer the sampling distribution of the means becomes normal.
- The standard deviation of the sampling distribution of the means will decrease making it approximately the same as the standard deviation of X as the sample size increases.

57.

*X*= the yearly income of someone in a third world country- the average salary from samples of 1,000 residents of a third world country
- $\stackrel{\u2013}{X}$ ∼
*N*$\left(\text{2000,}\frac{\text{8000}}{\sqrt{\text{1000}}}\right)$ - Very wide differences in data values can have averages smaller than standard deviations.
- The distribution of the sample mean will have higher probabilities closer to the population mean.
*P*(2000 < $\stackrel{\u2013}{X}$ < 2100) = 0.1537*P*(2100 < $\stackrel{\u2013}{X}$ < 2200) = 0.1317