Question

Practice Problem set 4 (Due Tuesday) Bonus points 3 Name Answer the following questions using the data gathered by researchers, from a random sample of undergraduate students during Spring 2015. 1. It is estimated that that Shoe size of adults 18-20 yrs. Follows a normal distribution with mean 9.5 and sd-2 (55 follows N(9.5, 2)). Test if this is true for the sample of 31 students using the 68, 95, 99.5 rule for normal distributions. Interval Number in this interval Percent in this interval (%) ut 10 ut 20 Lut 30 , What do you conclude? 2. As above, assuming that Shoe Size (SS) for young adults 18-20 follows normal distribution with N (9.5, 2). Answer the questions below: Draw a normal curve and shade the appropriate area for each. (This is for the entire American population not just our sample) a. What % of these young adults (YA) have SS of 9.5 or greater? b. What % of these young adults (YA) have SS between 9.5 and 11.57 c. If a YA is randomly chosen, what is the probability that his/her SS is less than 5.5? d. If a YA is randomly chosen, what is the probability that his/her SS is less than 9.0? e. Ifa YA is randomly chosen, what is the probability that his/her SS is greater than 10.07

Answer 1

1.

Interval	Number in this interval	Percent in this interval (%)
ulo (9.5 -2, 9.5 + 2) = (7.5, 11.5)	21	(21/31) * 100 = 67.74%
μΞ2σ (9.5 -2 * 2, 9.5 + 2 * 2) = (5.5, 13.5)	29	(29/31) * 100 = 93.55%
и+ Зо (9.5 -3 * 2, 9.5 + 3 * 2) = (3.5, 15.5)	31	(31/31) * 100 = 100%

The percentage values in the third column are almost equal to 68%, 95%, 99.5%.

We conclude that based on the sample data, the distribution of shoe size follows Empirical Rule.