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measurement and instruments 5 The marks on a statistics test are normally distri

ID: 3184089 • Letter: M

Question

measurement and instruments

5 The marks on a statistics test are normally distributed with a mean of 62 and a variance of 225. If the instructor wishes to assign B's or higher to the top 30% of the students in the class, what mark is required to get a B or higher? 6 The grade point averages of students at the University of Manitoba are approximately normally distributed with mean equal to 2.4 and standard deviation equal to 0.8. What fraction of the students will possess a grade point average in excess of 3.0? 7 The diameters of steel disks produced in a plant are normally distributed with a mean of 2.5 cm and standard deviation of.02 cm. The probability that a disk picked at random has a diameter greater than 2.54 cm is about: 8 Suppose the test scores of 600 students are normally distributed with a mean of 76 and standard deviation of 8. The number of students scoring between 70 and 82 is: 9 The lengths of pregnancies of humans are normally distributed with a mean of 268 days and a standard deviation of 15 days. Find the probability of a pregnancy lasting more tharn 300 days. 10 If Z is a standard normal random variable, find P (Z

Explanation / Answer

Solution7

mean=2.5

sd=0.02

P(x>2.54)

convert to z

z=x-mean/sd

z=2.54-2.5/0.02

z=2

P(Z>2)

=1-P(Z<2)

=1-0.9772

=0.0228

ANSWER:0.0228

Solution8:

n=600

mean=76

sd=8

P(70<X<82)

P(70-76/8<z<82-76/8)

=P(-0.75<Z<0.75)

=P(Z<0.75)-P(Z<-0.75)

=0.7734-(1-0.7734)

=0.5468

0.5468

NO OF STUDENTS=n*prob

=600*0.5468

=328.08

=328

NUMBER OF STUDENTS=328

Solution9:

mean=268

sd=15

P(X>300)

z=300-268/15

=2.13

P(Z>2.13)

=1-P(Z<2.13)

=1-0.9834

=0.0166

ANSWER:0.0166

Solution10:

P(Z<-1.3)

=1-P(Z<1.3)

=1-0.9032

=0.0968

ANSWER:0.0968