Question

2) Suppose the weight of a newborn baby follows a normal distribution with a mean of 3500 grams and a standard deviation of 600 grams.

a. What is the probability that the weight of a randomly selected newborn exceeds 4000g? b. For a random sample of 36 newborns, what is the probability that their mean weight is less than 3450g?

3) Suppose that 5% of American adults are vegetarian. Find the probability that in a random sample of 500 American adults, at least 20 are vegetarian.

4) Suppose the heights of American women are normally distributed with a mean of 64 inches and a standard deviation of 4 inches. What is the probability that a randomly selected American woman is between 64 and 69 inches tall?

5) Suppose that 80% of voters in a particular district are Republican. For a random sample of 250 voters, what is the probability that no more than 190 are Republican?

6) The heights of women are normally distributed. Suppose it is known that the population standard deviation is 2.5 inches.

a. Alice, a 63 inch tall woman, has a standard score of -0.32 for this distribution. Use this information to find the population mean.
b. If Bianca is 65 inches tall, compute the standard score for her height.

7) In order to estimate the population proportion, p, of defective transistors in a lot containing 100,000 transistors, a sample of size 800 is drawn yielding 5 defective transistors.

a. Use the sample to give a point estimate for p.
b. How large a sample would be required to estimate p within 0.1% at the 95% level of confidence?

8) A jar contains 5 coins: 2 pennies, 1 nickel, and 2 dimes. One coin will be randomly selected. If X equals the value (in cents) of the selected coin.

a. Find the table of probability distribution of X.

b. Find the expected value of X i.e E(X).

9. Consider the following game: A player rolls a fair, 6-sided, die. If the outcome is at least 3,  the player wins $1. Otherwise, the player loses $2. If X denotes the net winnings.

a. Find the table of probability distribution of X.

b. Find the expected value of X i.e E(X).

10. Seventy-five percent of the students graduating from high school in a small town in Oklahoma attend college. For a random sample of 50 students from the town, what is the probability that
a. at least 80% of the surveyed students will attend college?
b. between 80% and 85% (inclusive) of the surveyed students will attend college?

PLEASE HELP! ANYTHING WOULD BE APPRECIATED

Answer 1

Solution:-

2)

mean of 3500 grams and a standard deviation of 600 grams.

a) The probability that the weight of a randomly selected newborn exceeds 4000 g is 0.2023.

x = 4000

By applying normal distribution:-

z = 0.8333

P(z > 0.8333) = 0.2023

b) For a random sample of 36 newborns, the probability that their mean weight is less than 3450 g is 0.3085.

x = 3450

By applying normal distribution:-

z = - 0.50

P(z < - 0.50) = 0.3085

3) The probability that in a random sample of 500 American adults, at least 20 are vegetarian is 0.8728

P(Vegetarian) = 0.05

n = 500

x =20

By applying binomial distribution

P(x,n) = ⁿC_x*p^x*(1-p)^(n-x)

P(x > 20) = 0.8728