Question

17. Assume that the Richter scale magnitudes of earthquakes are normally distributed with a mean of 1.138 and a standard deviation of 0.586. Complete parts a through c below.

a. Earthquakes with magnitudes less than 2.000 are considered​ "microearthquakes" that are not felt. What percentage of earthquakes fall into this​ category? ___%

​(Round to two decimal places as​ needed.)

b. Earthquakes above 4.0 will cause indoor items to shake. What percentage of earthquakes fall into this​ category? ___

(Round to two decimal places as​ needed.)

c. Find the 95th percentile. ___

​(Round to three decimal places as​ needed.)

Will all earthquakes above the 95th percentile cause indoor items to​ shake?

A. Yes, because earthquakes above the 95th percentile are very rare and powerful.

B. Yes, because all earthquakes above the 95th percentile have magnitudes above 4.0.

C. No, because not all earthquakes above the 95th percentile have magnitudes above 4.0.

D. No, because no earthquakes above the 95th percentile have magnitudes above 4.0.

19. Chocolate chip cookies have a distribution that is approximately normal with a mean of 23.9 chocolate chips per cookie and a standard deviation of 2.8 chocolate chips per cookie. Find P5

and P95. How might those values be helpful to the producer of the chocolate chip​ cookies?

P5=____

(Round to one decimal place as​ needed.)

P95=___

(Round to one decimal place as​ needed.)

How might those values be helpful to the producer of the chocolate chip​ cookies? Choose the correct answer below.

A. The values can be used to identify cookies with an average number of chocolate​ chips, so those numbers can be used to monitor the production process to ensure that the numbers of chocolate chips stays within reasonable limits.

B. The values can be used to identify cookies with an unusually low or high number of chocolate​ chips, so those numbers can be used to monitor the production process to ensure that the numbers of chocolate chips stays below P 1.

C. The values can be used to identify cookies with an unusually low or high number of chocolate​ chips, so those numbers can be used to monitor the production process to ensure that the numbers of chocolate chips stays within reasonable limits.

D. The values can be used to identify cookies with an average number of chocolate​ chips, so those numbers can be used to monitor the production process to ensure that the numbers of chocolate chips stays below P 1

Answer 1

Ans:

a)

z=(2-1.138)/0.586

z=1.47

P(z<1.47)=0.9294 or 92.94%

b)

z=(4-1.138)/0.586

z=4.88

P(z>4.88)=0.0000 or 0.00%

c)

P₉₅=1.138+1.645*0.586=2.102

No, because no earthquakes above the 95th percentile have magnitudes above 4.0

19)

P₅=23.9-1.645*2.8=19.3

P₉₅=23.9+1.645*2.8=28.5

Option C is correct.

The values can be used to identify cookies with an unusually low or high number of chocolate​ chips, so those numbers can be used to monitor the production process to ensure that the numbers of chocolate chips stays within reasonable limits.