1). Answer the Following Given Bellow. A). Suppose X is a normal random variable
ID: 3350429 • Letter: 1
Question
1). Answer the Following Given Bellow.
A). Suppose X is a normal random variable with = 35 and = 10. Find P(21.4 < X < 39.7).
a) 0.2323
b) 0.5586
c) 0.2478
d) 0.5337
e) 0.5939
f) None of the above.
B). Laboratory experiment shows that the life of the average butterfly is normally distributed with a mean of 18.8 days and a standard deviation of 2 days. Find the probability that a butterfly will live between 12.88 and 15.76 days.
a) 0.0636
b) 0.0639
c) 0.0649
d) 0.0628
e) 0.0653
f) None of the above.
C). Endure All, a manufacturer of batteries claims that the lifetime of their batteries is normally distributed with a mean of 500 hours and a standard deviation of 40 hours. What is the probability that an Endure All battery selected at random will last more than 550 hours?
a) 0.1151
b) 0.8849
c) 0.8944
d) 0.1587
e) 0.1056
f) None of the above.
Explanation / Answer
A) Answer is (e) 0.5939
Calculations:
First calculate the Z score
Z score = (21.4-35)/10, (39.7-35)/10
=(-1.36,0.47)
Then find P(-1.36<Z<.47)
From the table, we get the value P(Z<-1.36)=.08691
P(Z<.47)=.68082
Then subtract .08691 from .68082,get the answer as .5939
B) Answer is (f) None of the above
First, calculate the Z score
Z score=(12.88-18.8)/2,(15.76-18.8)/2
=(-2.96,-1.52)
Then find P(-2.96<Z<-1.52)
From the table, we get the value P(Z<-2.96)=.00154
P(Z<-1.52)=.06426
Then subtract .00154from.06426 ,get the answer as .06272
C) Answer is (e) 0.1056
First, calculate the Z score
Z score=(550-500)/40=1.25
Then find the probability as P(Z>1.25)
From the table, we get the value P(Z>1.25)=.8944
therefore P(Z<1.25)=0.1056
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