Probability: 1263267

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