Question
Solution
Z value corresponding to 0.85 probability = 1.0364
Let the mean be M
Then , 1.0364 =( 16-M)/2
Solving for M , we get M = 13.93 ounces
Question
Solution
Z value for 0.9 probability = 1.2816
Hence, 1.2816 = (X -1865)/225
Solving the above, we get X = $2,153.35
Solution
Z = (3000-2210)/460 = 1.717
P (Z>1.717) = 1- P (Z<1.717) = 1- 0.957 = 0.043
Answer is 0.043
Question 4
Requisite probability = 0.5661/(0.1504+0.5661) = 0.7901
Question 5
Event C and R are not independent of each other. This is because the probability of event C is not the same for the two political affiliations i.e. R and D. If the leader has a R affiliation, then C would have probability of 0.37 but with D affiliation this probability of C reduces to 0.21. Hence, it is evident P(C) is a function of the political affiliation of the underlying leader.
Question 6
0.65 is c
0.28 is g
0.20 is a
1 is i
Question
Answer – probability is 0.22
Question 7
Answer is 0.33
Question 8
Answer is 45/365
Question 11
A and B are disjoint
Question 12
Total kittens = 8
Black kittens = 3
Non-black kittens = 8-3 = 5
Thus, in order to ensure that both kittens are non-black, the kittens have to be selected from the 5 kittens.
Hence, requisite probability = (5C2)/(8C2) = (5*4)/(8*7) = 5/14
Question 13
Yes it is possible for A and B to be disjoint since P(A) + P(B) is less than 1. Hence, there is no guarantee that some portion in the two sets would overlap with certainty.
Question
Solution
Expected number of cases = 1*0.02 + 2*0.03 +3*0.09 +4*0.55 +5*0.2+6*0.06 +7*0.05 = 4.26
Answer is 4.26
Question
Answer is 0.2537
Explanation
Required probability = P(0) + P(1) + P(2) = 25C0 (0.15)0(0.85)25 + 25C1 (0.15)1(0.85)24 + 25C2(0.15)2(0.85)23 = 0.2537
Question
Answer is Option A (No, because 89 is less than one standard deviation)
Question
Answer is 0.2023
Explanation
Z = (16-16.2)/0.24 = -0.8333
P (Z< -0.8333) = 0.2023 (As obtained from z table).
–
Question
Answer is 0.39
Explanation
Requisite probability = P(1) + P(2) + P(3) + P(4) = 0.02 + 0.03 +0.09 + 0.25 = 0.39
Question
Answer
Expected number = 4.26
Question
Mean = np = 55% * 300 = 165
Standard deviation = sqrt (npq) = sqrt (300*0.55 * 0.45) = 8.62