the annual sale of a fictional book is normally distributed with the unkown mean
ID: 3355668 • Letter: T
Question
the annual sale of a fictional book is normally distributed with the unkown mean and the unknown variance. Sales are Less than 1,000 copies 89.97% of the time and Less than 924 copies 69.85% of the time. a. what is the probability that the sales fall between 872 and 972 copies? b. what is the probability that the sales are greater than 700 copies? c. what is the probability that the sales are less than 800 copies? d. what is the probability that the sales are greater than 975? e. what is the probability that the sales are less than 722 copies? f. what is the probability that the sales are less than 400 or greater than 1,400 copies?
Explanation / Answer
Ans:
Given that
P(Z<=z)=0.8997
z=1.28
1.28=(1000-mean)/std. dev
mean+1.28*std dev=1000
Given that
P(Z<=z)=0.6985
z=0.52
0.52=(924-mean)/std dev
mean+0.52*std dev=924
subtract both eqn
0.76*std dev=76
std dev=100
mean+1.28*100=1000
mean=1000-128
mean=872
a)
z(872)=0
z(972)=(972-872)/100=1
P(0<=z<=1)=P(z<=1)-P(z<=0)=0.8413-0.5=0.3413
b)
z(700)=(700-872)/100=-1.72
P(z>-1.72)=P(z<1.72)=0.9573
c)
z(800)=(800-872)/100=-0.72
P(z<-0.72)=0.2358
d)
z(975)=(975-872)/100=1.03
P(z>1.03)=0.1515
e)
z(722)=(722-872)/100=-1.5
P(z<-1.5)=0.0668
f)
z(400)=(400-872)/100=-4.72
z(1400)=(1400-872)/100=5.28
P( z<-4.72 or z>5.28)=P(z<-4.72)+P(z>5.28)=0+0=0
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