Respuesta :
Answer:
The probability that no more than 70% would prefer to start their own business is 0.1423.
Step-by-step explanation:
We are given that a Gallup survey indicated that 72% of 18- to 29-year-olds, if given choice, would prefer to start their own business rather than work for someone else.
Let [tex]\hat p[/tex] = sample proportion of people who prefer to start their own business
The z-score probability distribution for the sample proportion is given by;
Z = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, p = population proportion who would prefer to start their own business = 72%
n = sample of 18-29 year-olds = 600
Now, the probability that no more than 70% would prefer to start their own business is given by = P( [tex]\hat p[/tex] [tex]\leq[/tex] 70%)
P( [tex]\hat p[/tex] [tex]\leq[/tex] 70%) = P( [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{0.70-0.72}{\sqrt{\frac{0.70(1-0.70)}{600} } }[/tex] ) = P(Z [tex]\leq[/tex] -1.07) = 1 - P(Z < 1.07)
= 1 - 0.8577 = 0.1423
The above probability is calculated by looking at the value of x = 1.07 in the z table which has an area of 0.8577.
