Question

The average weight of vegan men standing between 5 foot 9 inches and 5 foot 11 inches is 145lbs.with a standard deviation of 5 lbs. What are the minimum and maximum weights rounded to pounds for vegan men (in this height range) in the middle 78.5%?
a.) (141 lbs., 149 lbs.) b.) (134 lbs.,156 lbs.) c.) (139 lbs., 151 lbs.) d.) (150 lbs., 170 lbs.) e.) None of these.

When a convicted felon leaves prison and is on parole it can be a daunting task to find employment. Fortunately there exist farmers markets which offer employment suitable to recently paroled felons. At the Hermosa Beach farmers market 7 of the 13 farmers market employees are recently paroled felons. If the police select at random 4 employees at the Hermosa Beach farmers market what is the probability 2 of them are recently paroled felons?
a.) 0.4406 b.) 0.3381 c.) 0.3147 d.) 0.5454 e.) None of these

A ski resort losses $70,000 per season when it doesn’t snow very much and makes $250,000 profit when it does snow a lot. The probability of it snowing a lot is 40%. The expectation for the profit is
a.) $58,000 b.) $292,000 c.) $72,000 d.) $42,000 e.) None of these

Answer 1

1)

µ =    145                      
σ =    5                      
proportion=   0.7850                      
proportion left    0.2150   is equally distributed both left and right side of normal curve                   
z value at   0.1075   = ±   1.240   (excel formula =NORMSINV(   0.22   / 2 ) )  
                          
z = ( x - µ ) / σ                          
so, X = z σ + µ =                          
X1 =   -1.240   *   5   +   145   =   139
X2 =   1.240   *   5   +   145   =   151

answer: c.) (139 lbs., 151 lbs.)

2)

it is hypergeometric distribution          
and probability is given by           
P(X=x) =C(k,x)*C(N-k,n-x)/C(N,n)  

where   
Sample size,     n =    4
No. of events of interest in population    , k =   7
Population size   , N =   13

P(X=2)= C(7,2)*C (6,2)/C(13,4)           =   0.4406

3)

expected profit = ΣX*P(X) = 250000*(0.40)+(-70000)*(1-0.40)= $58,000

please upvote if it helps