Question

If 65 percent of the population of a large community is in favor of a proposed rise in school taxes, approximate the probability that a random sample of 100 people will contain:
(a) at least 50 who are in favor of the proposition;
(b) between 60 and 70 inclusive who are in favor;
(c) fewer than 75 in favor.

Answer 1

Answer:  a) 0.99917  b)  0.7054  c) 0.9820

Step-by-step explanation:

Let X denotes the number of people are in favor of a proposed rise in school taxes.

Era re given that p(probability that a person is in favor of a proposed rise )= 0.65

Sample size : n= 100

Mean= np = 100(0.65)=65

Standard deviation: $\sigma=\sqrt{np(1-p)}\\\\=\sqrt{100(0.65)(0.35)}\\\\=4.76969600708\approx4.77$

a) Now, the probability that a random sample of 100 people will contain  at least 50 who are in favor of the proposition :

$P(x\geq50)=P(\dfrac{x-\mu}{\sigma}\geq\dfrac{50-65}{4.77})\\\\=P(z\geq-3.144)\\\\=P(z-z)=P(Z$

b) between 60 and 70 inclusive who are in favor;

$P(60$

c) fewer than 75 in favor.

$P(x$