The life span of 100 W light bulbs manufactured by a company are tested. It is found that (8 %) of the light bulbs are rejected. A random sample of 15 bulbs is taken from stock and tested. The random variable X is the number of bulbs that is rejected.

a. Give four reasons why ? will have a binomial distribution.

b. Use a formula to find the probability that 2 light bulbs in the sample are rejected.

c. If the true probability of a rejected light bulb is 0.5340. Among the next 6 randomly selected bulbs, what is the probability that at least one of them is accepted?

d. If life span of light bulbs is adjusted so that the mean now is ?.

Find the value of ?:

i. Given that ?(?=0)=0.25.

ii. Given that the variance of ? is 2.4.

The speed of cars passing through the intersection of Blossom Hill Road and the Almaden Expressway varies from 12 to 35 mph and is uniformly distributed. None of the cars travel over 35 mph through the intersection.

a. Enter an exact number as an integer, fraction, or decimal.
μ =

b. σ =  (rounded to two decimal places)

c. What is the probability that the speed of a car is at most 26 mph?

d. What is the probability that the speed of a car is between 16 and 23 mph?

e. Find the 80th percentile. This means that 80% of the time, the speed is less than  mph while passing through the intersection.

f. Find the probability that the speed is more than 29 mph given (or knowing that) it is at least 16 mph.

PLEASE MAKE CLEAR STEPS.

The probability of having shortages of water on any given day is 0.12.

a. In the next ten days, what is the probability that we have water shortages in exactly two days?

b. What is the expected value of the number of days without water in the next ten days?

c. If an inspector arrives, and every day checks for water shortages, how many days on average will he have to maintain his inspection if he stops when he finds two days with water shortages?

d. What is the probability that we have to inspect between 15 and 20 days to get two days without water?

PLEASE MAKE CLEAR STEPS.

. Approximately 10% of all people are left-handed, then the rest of people are right-handed. Consider a group of 15 people, answer the following question: (You cannot use the binomial table for this problem) (a) State the random variable ?. (2 points) (b) Explain why this is a binomial experiment. There should be 4 conditions to check. (State the probability of left-handed people ?, the possible outcomes, and the number of trials ? in the conditions.) (4 points) (c) Find the probability that exactly three people are left-handed. (Round your answer to 4 decimal places) (6 points) (d) Find the probability that at least two people are left-handed. (Round your answer to 4 decimal places) (8 points)

Question 3. A sports club consists of 32% persons who play badmintonand 60% persons who play tennis. 10% of the sports club members playboth badminton and tennis. What is the --probability that a randomly selected person in the club plays neither tennis nor badminton?

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What is the number of non-negative integer solutions to the equation:

x1+x2+x3= 25

_____________

In answering a question on a multiple choice test, a studenteither knows the answer or the student just guesses. Suppose that theprobability that the student knows the answer is 0.75, and the probabil-ity that he guesses is 0.25. Assume that the probability that the student’sguesses will be correct is 0.20. What is the conditional probability thatthe student guessed the answer to a question given that he answered itcorrectly?

Suppose that only 0.1% of all computers of a certain type experience CPU failure during the warranty period. Consider a sample of 10, 000 computers. Let the random variable X equals the number of computers in the sample that have the defect. (a) What is the distribution of X? Write down its p.m.f.

(b) Give expression for the probability that exactly 56 computers will have the defect.

(c) What are the expected value and standard deviation of X?

(d) Approximate X by another distribution and give the p.m.f. of the approximated distribution.

(e) What is the approximate probability that more than 10 computers will have the defect?

(f) What is the approximate probability that between 10 and 20 (both inclusive) computers will have the defect?

A store gathers some demographic information from their customers. The following chart summarizes the age-related information they collected:

One customer is chosen at random for a prize giveaway.

Enter your answers as either decimals or fractions, not as percents.

What is the probability that the customer is at least 20 but less than 60?    

(Round to 4 places)

What is the probability that the customer is either older than 60 or younger than 30?    

(Round to 4 places)

What is the probability that the customer is at least 60?    

(Round to 4 places)

2. During the 2009 tax filing season, 15.8% of all individual U.S. tax returns were prepared by H&R Block. Suppose we randomly select 3 tax returns.

(a) Describe the probability distribution for X = the number in the sample whose returns were prepared by H&R Block. In other words, for each value of x, determine the associated probability.

(b) What is the mean and standard deviation, respectively, of X?

(c) For the probability distribution modeled in this question, is the assumption that we’re sampling with or without replacement? Explain.

(d) Suppose we wanted to use the normal approximation to the binomial distribution. What are the required conditions to use this approximation and are those conditions met here? Explain.

A particular type of tennis racket comes in a midsize version and an oversize version. Sixty percent of all customers at a certain store want the oversize version. (Round your answers to three decimal places.)

(a) Among ten randomly selected customers who want this type of racket, what is the probability that at least six want the oversize version?

(b) Among ten randomly selected customers, what is the probability that the number who want the oversize version is within 1 standard deviation of the mean value?

(c) The store currently has eight rackets of each version. What is the probability that all of the next ten customers who want this racket can get the version they want from current stock?

According to a recent study, 10 % of adult smokers started smoking before 21 years old. A random sample of 6 smokers age 21 years or older is selected, and the number of smokers who started smoking before 21 is recorded. Calculate the following probabilities. Round solutions to four decimal places, if necessary.

1. The probability that at least 3 of them started smoking before 21 years of age is

P(x≥3)=

2. The probability that at most 4 of them started smoking before 21 years of age is

P(x≤4)=

3. The probability that exactly 5 of them started smoking before 21 years of age is

P(x=5)=