contestada

The mean gas mileage for a hybrid car is 5656 miles per gallon. suppose that the gasoline mileage is approximately normally distributed with a standard deviation of 3.23.2 miles per gallon.​ (a) what proportion of hybrids gets over 6161 miles per​ gallon? (b) what proportion of hybrids gets 5252 miles per gallon or​ less? left parenthesis c right parenthesis what(c) what proportion of hybrids gets between 5858 and 6161 miles per​ gallon? (d) what is the probability that a randomly selected hybrid gets less than 4646 miles per​ gallon?

Respuesta :

CastleRook
To solve the questions we proceed as follows:
z=(x-μ)/σ
a] Proportion of hybrid that gets over 61 miles per gallon
z=(61-56)/3.2
z=1.5625
thus
P(X≥61)=1-P(X≤61)
P(X≤61)=0.9406
thus:
P(X≥56)=1-0.9406=0.0594

b]what proportion of hybrids gets 52 miles per gallon or​ less? 
z=(52-56)/3.2=-1.25
P(X≤52)=0.1056

c] what proportion of hybrids gets between 58 and 61 miles per​ gallon?
here we need to calculate:
P(58≤X≤61)
P(X≤61)=0.9406

P(X≤58) will be given by:
z=(58-56)/3.2=0.625
P(X≤58)=0.7357
thus:
P(58≤X≤61)=0.9406-0.7357=0.2049

d]what is the probability that a randomly selected hybrid gets less than 46 miles per​ gallon?
z=(46-56)/3.2
z=-3.125
P(X≤46)=0.0009

Otras preguntas