Question

How do you do question 23?

u, lilas meanl.s ounces and standard deviation 0.125 ounce, what proportion of the pucks will be usable in professional games? 20. Hockey pucks used in professional hockey games must weigh between 5.5 and 6 ounces. f the weight of pucks manufactured by a particular process is bell-shaped and has mean 5.75 ounces, how large can the standard deviation be if 99.7% of the pucks are to be usable in professional games? 22. Suppose that, as in the previous exercise, speeds of vehicles on a section of highway have mean 60 mph and standard deviation 2.5 mph, but now the distribution of speeds is unknown. a. if the speed limit is 55 mph, at least what proportion of vehicles must speeding? b. What can be said about the proportion of vehicles going 65 mph or faster? 23. An instructor announces to the class that the scores on a recent exam had a bell-shaped distribution with mean 75 and standard deviation 5. a. What is the median score? b. Approximately what proportion of students in the class scored between 70 and 80? C. Approximately what proportion of students in the class scored above 85? d. What is the percentile rank of the score 85? ently registered students at a large university have a bell-shaped distribution with 24. The GPAs of all curr n 2.7 and standard deviation 0.6. Students with a GPA below 1.5 are placed on academic probation. tely what percentage of currently registered students at the university are on academir Ap

Answer 1

Solution23a:

for bell shaped or normal distribution

mean=median=mode

median=75

Soluton23b:

P(70<X<80)

get z scores as z=x-mean/sd

P(70-75/5<z<80-75/5)

P(-1<z<1)

P(Z<1)-P(Z<-1)

=0.8413-(1-0.8413)

=0.6826

ANSWER:

0.6826

Soution2c:

P(X>85)

P(Z>85-75/5)

P(Z>10/5)

P(Z>2)

=1-P(Z<2)

=1-0.9772

=0.0228

ANSWER:

0.0228

Solutiond:

z=x-mean/sd

=85-75/5

z=2

using r code to get percentile rounded of

round(pnorm(2)*100,0)

= 98

ANSWER:98 PERCENTILE