6.4 Binomial Distribution
A quality control inspector has drawn a sample of 18 light bulbs from a recent production lot. Suppose 20% of the bulbs in the lot are defective. What is the probability that between 7 and 11 (both inclusive) bulbs from the sample are defective? Round your answer to four decimal places.
answer 0.0512 P(x=7,8,9,10,11) using binomial formula and add them up
A quality control inspector has drawn a sample of 18 light bulbs from a recent production lot. Suppose 30% of the bulbs in the lot are defective. What is the probability that between 8 and 12 (both inclusive) bulbs from the sample are defective? Round your answer to four decimal places.
answer 0.1404 P(x=8,9,10,11,12) using binomial formula and add them up
A quality control inspector has drawn a sample of 5 light bulbs from a recent production lot. Suppose that 30% of the bulbs in the lot are defective. What is the standard deviation of the number of defective bulbs in the sample? Round your answer to two decimal places.
answer 1.02 sd=sqrt(n*p*(1-p)) n=5 p=.7 1-.7=.3
The random variable X is a binomial random variable with n=4 and p=0.9. What is the expected value of X? Do not round your answer.
answer 3.6 expected value = 3.6 =n*p =4*0.9
The Alvin Secretarial Service procures temporary office personnel for major corporations. They have found that 40% of their invoices are paid within ten working days. A random sample of 18 invoices is checked. What is the probability that exactly 3 of the invoices will be paid within ten working days? Round your answer to four decimal places.
answer =0.0246 use binomial formula with p=0.40 n=18
Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places P(X=15), n=18,p=0.8
=ROUND(BINOM.DIST(15,18,0.8,FALSE),4) answer .2297
In manufacturing integrated circuits, the yield of the manufacturing process is the percentage of good chips produced by the process. The probability that an integrated circuit manufactured by the Ace Electronics Company will be defective is p=0.02. If a random sample of 12 circuits is selected for testing, answer the following questions. Step 1 of 2 : What is the probability that no more than one integrated circuit will be defective in the sample? Round your answer to four decimal places, if necessary.
P(X=0,1) n=12 p=0.02 use binomial formula Apply the binomial probability formula: P(X=x)=ncx×px×(1−p)n−x
