Ages of pennies. The histogram below shows the distribution of ages of pennies a
ID: 3257862 • Letter: A
Question
Ages of pennies.
The histogram below shows the distribution of ages of pennies at a bank.
(a) Describe the distribution.
Left skewed
Right skewed
Symmetric
Sampling distributions for means from simple random samples of 5, 30, and 100 pennies is shown in the histograms below.
When the sample size is small, the sampling distribution is right skewed, just like the population distribution. As the sample size increases, the sampling distribution gets more unimodal, symmetric, and approaches normality. The variability also decreases. This is consistent with the Central Limit Theorem.
The mean age of the pennies is 10.44 years, with a standard deviation of 9.2 years. Using the Central Limit Theorem, calculate the means and standard deviations of the distribution of means from random samples of size
(b) 5
x¯=x¯= s=s=
(c) 30
x¯=x¯= s=s=
(d) 100
x¯=x¯= s=s=
Explanation / Answer
a) Right Skewed Distribution because it has long tail on right side
b) n = 5
Mean = 10.44 yrs
Standard deviation = 9.2/Sqrt(5) = 4.114 yrs
(c) n = 30
Mean = 10.44 yrs
Standard deviation = 9.2/Sqrt(30) = 1.6797 yrs
(d) n = 100
Mean = 10.44 yrs
Standard deviation = 9.2/Sqrt(100) = 0.92 yrs