Example 7.6 from Statistics, 7.2 The Central Limit Theorem for Sums (Optional)

The Central Limit Theorem for Sums (Optional): example 7.6

In a recent study reported Oct. 29, 2012, the mean age of tablet users is 34 years. Suppose the standard deviation is 15 years. The sample size is 50.

What are the mean and standard deviation for the sum of the ages of tablet users? What is the distribution?
Find the probability that the sum of the ages is between 1,500 and 1,800 years.
Find the 80^th percentile for the sum of the 50 ages.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1
Solution
1. μ_Σx = nμ_x = 50(34) = 1,700 and σ_Σx = $\sqrt{n}$ σ_x = $(\sqrt{50})$ (15) = 106.01
  The distribution is normal for sums by the central limit theorem.
2. P(1500 < Σx < 1800) = normalcdf (1500, 1800, (50)(34), $(\sqrt{50})$ (15)) = 0.7974
3. Let k = the 80^th percentile.
  k = invNorm(0.80,(50)(34), $(\sqrt{50})$ (15)) = 1789.3

How did it go?

Solution

Solution