1. (15 Points) On the average, City Bank approves 30% of all its personal loan a
ID: 2907185 • Letter: 1
Question
1. (15 Points) On the average, City Bank approves 30% of all its personal loan applications. On a particular day there are 15 loan applications. Using the binomial distribution charts find the following probabilities:
a. Exactly five loans are approved? ___________________________________________________________________
b. Ten or more loans are approved? ________________________________________
c. Less than two loans are approved?________________________________________
2. (20 points) IQ data is thought to be normally distributed with a mean of 100 and a standard deviation of 15.
a. Using the empirical rule, what is the IQ range we would expect approximately 95% of the population to be? _____________________________________________________________________
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b. Make a sketch of the IQ distribution and using the normal z chart, find the probability of having an IQ greater than 132. This is the minimum Stanford-Binet IQ score required to join Mensa, the largest high IQ society in the world. ________________________________________________________________________
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c. The average IQ score of US College graduates is 115. Based on the given IQ data, what is the percentage of the US population that has IQ’s below 115? _____________________________________________________________________
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Explanation / Answer
As per company policies are in answering question 1 only
P(X=x) = nCx * p^x * q^(n-x)
P= 30.00%
n= 15
a)
P(X=x)
=P(X=5)
=BINOM.DIST(5,15,0.3,FALSE)
0.206
b)
P(X>=10)
1-P(X<10)
1-P(X<=9)
=1-BINOM.DIST(9,15,0.3,TRUE)
0.0037
c)
P(X<2)
P(X<=1)
P(X=0)+P(X=1)
BINOM.DIST(1,15,0.3,TRUE)
0.0353
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