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 (ZExplanation / 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
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