A study was carried out to determine the number of women using folic acid supplements in early pregnancy. All women attending a public or private clinic in Ohio were invited to participate and 28 women accepted. Based on previous studies, we know that typically 62% of pregnant women take folic acid supplements during early pregnancy.

a) What is the probability that exactly 25 women take a folic acid supplement during early pregnancy? (Use formula/show work, NOT binompdf or binomcdf.)

b) What is the probability that more than 21 women take folic acid supplements using early pregnancy? (Use binomcdf or binompdf. State function and its arguments.)

c) What is the probability that at least 15, but less than 20 women take folic acid supplements during early pregnancy? (Use binomcdf or binompdf. State function and its arguments.)

An airline company operates commuter flights using an aircraft that can take 20 passengers. During each flight passengers are given a hot drink and a Snack Pack that contains a meat sandwich and a cake. The company is aware that some of their passengers may be vegetarians and therefore every flight should be stocked with vegetarian Snack Pack that contains a cheese sandwich in addition to those contain meat. Given that 5% of the population is vegetarian, on a fully booked flight, answer the following questions.                                                                                                                    

a) What is the expected number and standard deviation of vegetarian passenger?

b) What is the probability that there will be exactly one vegetarian passenger? * ANSWER USING EXCEL FUNCTIONS *

c) What is the probability that there will be more than one vegetarian passenger? * ANSWER USING EXCEL FUNCTIONS *

d) What is the probability that there will be no more than two vegetarian passenger? * ANSWER USING EXCEL FUNCTIONS *

With the COVID-19 crisis, a manager is concerned with handling the amount of customers arriving to his store. The manager assumes that the number of customers, X, arriving per hour has a Poisson distribution with mean rate of 10 customers per hour. Use this distribution for exercises!

1. Use R to generate the pmf of X.

2. Use R to plot the pmf of X.

3. Give the probability that at least 11 customers arrive to the store in a given hour.

4. There are 10 cards face down on a table and 3 of them are aces. If 5 of these cards are selected at random, what is the probability that at least 2 of them are aces?

5. Defects in a certain type of aluminum screen appear on the average of one in 150 square feet. If we assume the Poisson distribution, find the probability of at most one defect in 230 square feet.

Parts are inspected on a production line for a defect. It is known that 5% of the pieces have this defect. (this applies to 5 parts of the problem)

a. If an inspector examines 12 parts, what is the probability of finding more than 2 defective parts?

b. What is the expected number of defective parts in 12-piece sample?

C. In another area, parts are inspected until 5 defective parts are found, then the machine is stopped to reset the machine. Does the machine stop on average every time parts?

d. In another area, parts are inspected until 3 faulty parts are found, then the machine is stopped to reset the machine. What is the probability of needing between 55 and 60 pieces to stop the machine?

e. 100 pieces were separated for special tests. A sample of 15 pieces will be taken from these 100. What is the probability of finding at least 2 defects in the sample?

Seventy percent of the students applying to a university are accepted. Using the binomial probability tables or Excel, what is the probability that among the next 12 applicants:

1. At least 6 will be accepted?
2. Exactly 10 will be accepted?
3. Exactly 8 will be rejected?
4. Seven or more will be accepted?
5. Determine the expected number of acceptances.
6. Compute the standard deviation.  Hint from Dr. Klotz: There are formulas you need on page 245 or check out 5.4 in Notations and Symbols for this week. Remember that standard deviation is the square root of the variance.

Scores on a recent national statistics exam were normally distributed with a mean of 90 and a standard deviation of 5.

1. What is the probability that a randomly selected exam will have a score of at least 85?
2. What percentage of exams will have scores between 89 and 92?
3. If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award?

Although studies continue to show smoking leads to significant health problems, 30% of adults in a country smoke. Consider a group of 250 adults, and use the normal approximation of the binomial distribution to answer the questions below.

(a)What is the expected number of adults who smoke?

75  adults

(b)What is the probability that fewer than 65 smoke? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)

(c)What is the probability that from 80 to 85 smoke? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)

(d) What is the probability that 100 or more smoke? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)

This question has been answered but the answers are incorrect

You have 3 coins that look identical, but one is not a fair coin. The probability the unfair coin show heads when tossed is 3/4, the other two coins are fair and have probability 1/2 of showing heads when tossed.

You pick one of three coins uniformly at random and toss it n times, (where n is an arbitrary fixed positive integer).

Let Y be the number of times the coin shows heads. Let X be the probability the coin you choose shows heads when flipped. (Note that X is a random variable because you’re randomly choosing a coin).

a) What is the pmf of X?

b) For each x that the random variable X can equal, give the conditional distribution of Y given X = x.

c) Determine the unconditional distribution of Y .

d) Compute the expectation of Y

Suppose you play a "daily number" lottery game in which three digits from 0–9 are selected at random, so your probability of winning is 1/1000. Also suppose lottery results are independent from day to day.

A. If you play every day for a 7-day week, what is the probability that you lose every day?

B. If you play every day for a 7-day week, what is the probability that you win at least once? (Hint: Make use of your answer to part a.)

C. Repeat parts a and b if you play every day for a 30-day month.

D. What if each digit can only be selected once. How many different ways can the three digits be selected?

E. If order does matter in the digits, how many different ways can the numbers be arranged?

1. 1000 used car tires are being evaluated by a major insurance company. The quality of the tiers are based on the depth of the treads and years in use. The results from 1000 tires are summarized as the following:

Let A denote the event that a tire is new (less than 2 years old), and let B denote the tire has low depth for treads (less than 3 mm). Determine the number of castings in

1. Put in writing what A∩ B means.
2. Find A∩ B
3. Find A∪ B¢
4. What is the probability that a randomly selected tire is not new with high treads depth?
5. What is the probability that a randomly selected tire is not new with low treads depth?
6. If a selected tire was found to be new, find the probability that it is with high treads depth.
7. Find P(A | B)

This is the first question and I know how to solve this one, but I am confused by the second one (The admissions office of a small, selective liberal-arts college will only offer admission to applicants who have a certain mix of accomplishments, including a combined SAT score of 1,300 or more. Based on past records, the head of admissions feels that the probability is 0.58 that an admitted applicant will come to the college. If 500 applicants are admitted, what is the probability that 310 or more will come? Note that “310 or more” means the set of values {310, 311, 312, …, 500}. )

The following is the second question

Consider the admissions office in the previous problem. Based on financial considerations, the college would like a class size of 310 or more. Find the smallest n, number of people to admit, for which the probability of getting 310 or more to come to the college is at least 0.95.