Intro to Stats and Analytics

Question

Suppose that wedding costs in the Caribbean are normally distributed with a mean of $7000 and a standard deviation of $950. Using the Empirical rule below, estimate the percentage of Caribbean weddings that cost

(You do not need to round your values)

(a) between $4150 and $9850.  %

(b) above $9850.  %

(c) below $5100.  %

(d) between $6050 and $9850.  %

Answer 1

Hi Lucy,

The Empirical Rule is also known as the 68-95-99.7 Rule. It states that for normally distributed data, 68% of observations fall within one standard deviation (sigma) of the mean(mu), 95% fall within two, and 99.7% fall within three. With that in mind, let's work the problem:

a. mu=7000, sigma=950

4150 is three standard deviations below 7000. 9850 is three standard deviations above. Just do the addition and subtraction: 7000 +/- 950 +/- 950 +/- 950 = (4150, 9850)

We know from the Empirical Rule that 99.7% of data falls within three standard deviations either way, so your final answer here is: 99.7%

b. We know that 99.7% of data falls between 4150 and 9850 from above. That means we have 0.03 percent of the data left over. If you look at the graph of the 68-95-99.7 Rule, you will see the very small sections at either end. Each of those sections represent half of 0.03, or 0.015, which means that upper segment above 9850 is 0.15%.

c. 5100 is two standard deviations below the mean, and we know 95% of data falls within two standard deviations either way. So we want below that. That means 5% of the data falls below that cutoff in both directions, but we are interested only in the low end, so: we now divide that by 2 to get 2.5%. .

d. 6050 is one standard deviation below 7000 (7000 - 950 = 6050). 9850 is three standard deviations above (7000 + 3(950) = 9850). So, to get the lower portion, we divide the 68% from the Empirical Rule by 2 and get 34%. To get the upper portion, we divide 99.7 by 2 to get 49.85%. Total is the sum: 34 + 49.85 = 83.85%

I hope this helps.