More Probability Practice Group Names From Census data, it is known that 51% of

Question

More Probability Practice Group Names From Census data, it is known that 51% of adult Americans are women. What is the probability that an adult American chosen at random is a woman? Suppose a random sample of 100 adult Americans will be collected. The gender of each of the 100 p, will be calculated. What is the mean of the sampling distribution of the sample proportion? What is the Standard Deviation of the sampling distribution of the sample proportion? is the distribution of the sample proportion approximately normal? Justify your response be providing a calculation or calculations. What is the probability that the sample proportion will be greater than 52? What is the probability that the sample proportion will be less than 48 What is the probability the sample proportion will be between 47 and.53?

Explanation / Answer

the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd/sqrt(n) ~ N(0,1)
a.
mean = proportion ( p ) = 0.5
b.
standard Deviation ( sd )= sqrt(PQ/n) = sqrt(0.5*0.5/100)
=0.05
c.
Points to pass for normal approximation:
1) experiment consistes of a sequence of n identical trials
2) only 2 outcomes are possible on each trail, success or failure
3) trials are independent & below conditions should satisfy
n*p>5, 100*0.5> 5 => 50>5
n*(1-p)>5, 100*0.5> 5 => 50>5
can use normal approximation

d.
GREATER THAN
P(X > 0.52) = (0.52-0.5)/0.05
= 0.02/0.05 = 0.4
= P ( Z >0.4) From Standard Normal Table
= 0.3446

d.
LESS THAN
P(X < 0.48) = (0.48-0.5)/0.05
= -0.02/0.05= -0.4
= P ( Z <-0.4) From Standard Normal Table
= 0.3446
e.
BETWEEN THEM
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 0.47) = (0.47-0.5)/0.05
= -0.03/0.05 = -0.6
= P ( Z <-0.6) From Standard Normal Table
= 0.27425
P(X < 0.53) = (0.53-0.5)/0.05
= 0.03/0.05 = 0.6
= P ( Z <0.6) From Standard Normal Table
= 0.72575
P(0.47 < X < 0.53) = 0.72575-0.27425 = 0.4515

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.