(p. 104). The article highlights the downside risks to future real house price growth in 22 advanced economies and 10 emerging market economies. For 2,384 advanced economies, the mean and standard deviations of the quarterly change rate are .48% and 2.36% respectively, while for 960 emerging market economies, the mean and standard deviations of the quarterly change rate are .63% and 3.02% respectively. Assume that the quarterly change rate in real house price for both types of economy is approximately normal.

a. For the advanced economies, find the probability that the quarterly change rate in real house price is less than .5%.

b. For the emerging market economies, find the probability that the quarterly change rate in real house price is less than .5%.

c. What is the minimum quarterly change rate in real house price of the advanced economies for 10% of the observations?

d. Repeat part c for the emerging market economies.

e. By observing the quarterly change rate in real house price for both types of economy, what inferences can you make of the likelihood of quarterly change rate being less than .5%? 4.106 Voltage sags and swells. Refer to the Electrical Engineering (Vol. 95, 2013) study of the power quality of a transformer, Exercise 2.111 (p. 118). Recall that two causes of poor power quality are “sags” and “swells.”. (A sag is an unusual dip and a swell is an unusual increase in the voltage level of a transformer.) For Turkish transformers built for heavy industry, the mean number of sags per week was 353 and the mean number of swells per week was 184. As in Exercise 2.111, assume the standard deviation of the sag distribution is 30 sags per week and the standard deviation of the swell distribution is 25 swells per week. Also, assume that the number of sags and number of swells are both normally distributed. Suppose one of the transformers is randomly selected and found to have 400 sags and 100 swells in a week.

a. What is the probability that the number of sags per week is less than 400?

b. What is the probability that the number of swells per week is greater than 100? 4.107 Gender bias in online job image searches. Are females and males depicted equally in online images of the workplace? Not according to the results of a Pew Internet Research (December 2018) study of online images for hundreds of jobs. For each job, the researchers searched and analyzed the first 100 workplace images. One result: males are overrepresented (and women underrepresented) on the searched images for the majority of jobs. In addition, the search position of the image showing the first female (and male) was determined. Since 100 workplace images were studied, the search position ranged from 1 to 100. (Example: For one job, the first picture of a female occurred with the fifth image; thus, the 1st-female-image position for this job is 5.) When averaged across jobs, the 1st-female-image position had a mean of 3.7 and the 1st-male-image position had a mean of 2.0. Assume that the standard deviation is .5 for both, and that both distributions are approximately normal.

a. For a randomly selected job, what is the probability that the 1st-female-image position is 2 or less?

b. For a randomly selected job, what is the probability that the 1st-male-image position is 2 or less? 4.108 Safety of underground tunnels. Research published in the journal Tunnelling and Underground Space Technology (July 2014) evaluated the safety of underground tunnels built in rigid soils. A factor of safety (FS), measured as the ratio of capacity over demand, was determined for three different areas of tunnels made from shotcrete: tunnel face, tunnel walls, and tunnel crown. FS was determined to be normally distributed in each area, with means and standard deviations shown in the table. Tunnel failure is considered to occur when FS is lower than or equal to 1. Which tunnel area is more likely to result in failure? Why? Mean (m) Standard Deviation (s) Tunnel Face 1.2 .16 Tunnel Walls 1.4 .20 Tunnel Crown 2.1 .70 4.109 Sports and other outdoor activities. Refer to the sports and outdoor activities survey conducted by Statistics Norway, Exercise