The proportion of adult women in the United States is approximately 51%. A marke
ID: 3360772 • Letter: T
Question
The proportion of adult women in the United States is approximately 51%. A marketing survey telephones 500 people at random. 1. (a) (3pts) What is the sampling distribution of the observed proportion that are women? State your answer with the mean and the standard deviation. (b) (3pts) would you be surprised to find 56% wom en in a sample of size 500? Explain. (c) (2pts) what is the probability that more than 53% women in this survey? (d) (2pts) What is the probability that there were fewer than 180 women in the sample? (e) (2pts) What is the probability that there were between 225 and 300 women in the sample? Human gestation times have a mean of about 266 days with a standard deviation of about 16 days. Suppose we look from many random samples of 200 women. (a) (2pts) f we made the histogram of all these sample means, what shape would it have? 2. at the mean gestation times for many samples of 200 women. Image all the possible values of the sample mean (b) (2pts) What is the probability that a sample of 200 women has a mean gestation time of 250 days or less? (c) (2pts) What is the probability that a sample of 200 women has a mean gestation time of 270 days or more? (d) (3pts) What is the number of days in the gestation time for a sample of 100 women if you want to know the 20 percentile?Explanation / Answer
1)
a) proportion of women 'p' follows normal distribution with
mean = np = 500 * 0.51 = 255
standard deviation = sqrt(npq) = sqrt(500 * 0.51 0.49) = 11.178
b) 56% of 500 = 280
using binomial distribution
p [x = 280] = 500c280 0.51280 0.49220 = 0.0002
given event has very less chance
c) 53% of 500 = 265
using normal apporximation to the binomial
p [X > 265] = p [Z > 265 - 255/11.178] = p [Z > 0.895] = 0.1854
d) p [x < 180] = p [Z < 180 - 255/11.178] = p [Z < -6.71] = 0.0000[unusual event]
e) p[225 < x < 300] = p [225- 255/11.178 < Z < 300-255/11.178] = p[-2.684 < Z < 4.026] = 0.9963
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.