The overhead reach distances of adult females are normally distributed with a mean of 195 cm and a standard deviation of 7.8 cm. a. Find the probability that an individual distance is greater than 207.50 cm. b. Find the probability that the mean for 25 randomly selected distances is greater than 193.20 cm. c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30? a. The probability is _______

Please post all the work so I can understand the process! Thanks :)

Question 3:

The 9-month salaries at a daycare center are normally distributed with a mean of $18,000 and a standard deviation of $5,000.

A test for diabetes classifies 99% of people with the disease as diabetic and 10% of those who don't have the disease as diabetic. It is known that 12% of the population is diabetic.

a) what are the false positive and false negative rates?

b) what is the probability that someone classified as diabetic does in fact have the disease?

i) solve the problem by drawing up a contingency table and

ii) solve the problem using conditional probability and the law of total probability

The wait time at the Goleta Post Office is uniformly distributed between 1 and 16 minutes.

a) Define the random variable of interest, X.

b) State the distribution of X.

c) What is the average wait time?

d) Calculate the probability that the wait time is more than 17 minutes.

e) Calculate the probability that the wait time is at least 10 minutes.

f) Calculate the probability that the wait time is between 2 and 11 minutes

It is known that of the articles produced by a factory, 20% come from Machine A, 30% from Machine B, and 50% from Machine C. The percentages of satisfactory articles among those produced are 95% for A, 85% for B and 90% for C. An article is chosen at random. (a) What is the probability that it is satisfactory? (b) Assuming that the article is satisfactory, what is the probability that it was produced by Machine A? (c) Given that the article is satisfactory, what is the probability that it was produced by Machine C?

Jobs arrive at the server is a Poisson random variable with a mean of 360 jobs per hour. Find:

1. The probability of at least 8 jobs arriving in the interval [8:00, 8:02] a.m.
2. The probability of at most 8 jobs arriving in the interval [9:15, 9:18] p.m.
3. Using the exponential distribution (and its relation to the Poisson) find the probability of no jobs arriving in the interval [7:00, 7:01] p.m.

During a blood-donor program conducted during finals week for college students, a blood-pressure reading is taken first, revealing that out of 200 donors, 28 have hypertension. All answers to three places after the decimal. A 95% confidence interval for the true proportion of college students with hypertension during finals week is (WebAssign will check your answer for the correct number of significant figures. Incorrect: Your answer is incorrect. , WebAssign will check your answer for the correct number of significant figures. Incorrect: Your answer is incorrect. ). We can be 80% confident that the true proportion of college students with hypertension during finals week is WebAssign will check your answer for the correct number of significant figures. Incorrect: Your answer is incorrect. with a margin of error of WebAssign will check your answer for the correct number of significant figures. Incorrect: Your answer is incorrect. . Unless our sample is among the most unusual 10% of samples, the true proportion of college students with hypertension during finals week Is between WebAssign will check your answer for the correct number of significant figures. Incorrect: Your answer is incorrect. and WebAssign will check your answer for the correct number of significant figures. Incorrect: Your answer is incorrect. . The probability, at 60% confidence, that a given college donor will have hypertension during finals week is WebAssign will check your answer for the correct number of significant figures. Incorrect: Your answer is incorrect. , with a margin of error of WebAssign will check your answer for the correct number of significant figures. Incorrect: Your answer is incorrect. . Assuming our sample of donors is among the most typical half of such samples, the true proportion of college students with hypertension during finals week is between WebAssign will check your answer for the correct number of significant figures. Incorrect: Your answer is incorrect. and WebAssign will check your answer for the correct number of significant figures. Incorrect: Your answer is incorrect. . We are 99% confident that the true proportion of college students with hypertension during finals week is WebAssign will check your answer for the correct number of significant figures. Incorrect: Your answer is incorrect. , with a margin of error of WebAssign will check your answer for the correct number of significant figures. Incorrect: Your answer is incorrect. . Assuming our sample of donors is among the most typical 99.9% of such samples, the true proportion of college students with hypertension during finals week is between WebAssign will check your answer for the correct number of significant figures. Incorrect: Your answer is incorrect. and WebAssign will check your answer for the correct number of significant figures. Incorrect: Your answer is incorrect. . Covering the worst-case scenario, how many donors must we examine in order to be 95% confident that we have the margin of error as small as 0.01? Incorrect: Your answer is incorrect. Using a prior estimate of 15% of college-age students having hypertension, how many donors must we examine in order to be 99% confident that we have the margin of error as small as 0.01? Incorrect: Your answer is incorrect.

The J.O. Supplies Company buys calculators from a Korean supplier. The probability of a defective calculator is 15%. If 16 calculators are selected at random, what is the probability that more than 5 of the calculators will be defective?

There are 36 students in the classroom. Assuming each date of the year are equally

likely to be the birthday of a student. Calculate the probability that there are at least

two students having the same birthday.

use probability and stats to solve