Statistics and Probability Answers

In 1983, a random sample of 1000 scientists included 212 female scientists. A similar
random sample of scientists in 1990 included 272 women. Do these figures indicate
an increase in the population proportion of scientists who are women?

Hint: Construct the 95% CI for the difference in proportions and examine whther
that CI contains zero.

Consider an additive white Gaussian noise channel with an expected output power constraint P. Thus, Y = X + Z, Z is normally distributed with mean 0 and variance of s^2. Z is independent of X and the expected value of Y^2 <= P. Find the channel capacity.

The compressive strength of cement is assumed to be normally distributed with a mean of 8000 kilograms per sq cm and a standard deviation of 200 kilograms per sq. cm.
a) Find the probability that the strength is less than 8200 kg per sq. cm
b) Find the probability that the strength is between 7500 and 7700 kg per sq. cm
c) Determine the value for which the probability that the strength of cement is below this value is 90%.

In a study for Health Statistics, it was found that the mean height of female 20-25 years old was 64.1 inches. If height is normally distributed with a standard deviation of 2.8 inches.
a) Determine the height required to be in the top 10% of all 20-25 years old females.
b) A “one-size-fits all” robe is being designed that should fit 90% of 20-25 years old females; what heights constitute the middle 90% of all 20-25 years old females?

1. Find the z-score if the area under a standard normal curve to the right of z is 0.09

Two interviewers were asked to interview 9 candidates for a prospective Job. They were supposed to independently rank each candidate numerically. (I don't knw if the numer of questions is relevant but for the sake of argument say there were 10 questions) What is the probability of both interviewers ending up with the first 7 out of 9 candidates ranked eaxactly the same in the final ranking of all candidates?

I have 4 blocks which I will run sequentially (block 1,2,3,4).
Is it necessary or is it incorrect to randomize the run order within the blocks?

8 men in a company of 25 are graduate. If 3 mens are picked out of the 25 at random. What is the probability that at best 1 graduate?

The resistances produced by a manufacturer follow a normal distribution with a mean of 150 ohm and standard deviation = 5ohm What percentage of resistors will have a resistance between 140ohm and 160ohm?

Six students are selected at random and provided an overview of an assessment of its rational, length, question format, and so on. The remaining five students are not given the overview. The scores are:

overview provided: 20, 18, 14, 22, 16, 16

no overview provided: 11,15,16,13,9

a. set up H0 and H1

b. perform test at alpha = 0.01

c. draw final conclusion.