Question

In: Statistics and Probability

3.5.18. A shirt manufacturer knows that, on the average, 2% of his product will not meet...

3.5.18. A shirt manufacturer knows that, on the average, 2% of his product will not meet quality specifications. Find the greatest number of shirts constituting a lot that will have, with probability 0.95, fewer than five defectives.

Question is from a chapter on Central Limit Theorem and Chebyshev’s theorem.

Solutions

Expert Solution

Here if the number of shirts are = n

Pr(Defective) = 0.02

so here expective number of deffective shirts = 0.02n

standard deviation of number of defective shirts = (0.02 * 0.98 * n)

so here, by using the central limit theorem

Pr(X < 5 ; 0.02n; 0.14 n] = 0.95

Z value = 1.645

(5 - 0.02n)/ (0.14n) = 1.645

5 - 0.02n = 0.23 sqrt (n)

5 - 0.02n = 0.23

25 + 0.0004n2 - 0.2529n = 0

so here by solving it we get

n = 122.27 or 123


Related Solutions

John knows that monthly demand for his product follows a normal distribution with a mean of...
John knows that monthly demand for his product follows a normal distribution with a mean of 2,500 units and a standard deviation of 425 units. Given this, please provide the following answers for John. a. What is the probability that in a given month demand is less than 3,000 units? b. What is the probability that in a given month demand is greater than 2,200 units? c. What is the probability that in a given month demand is between 2,200...
John knows that monthly demand for his product follows a normal distribution with a mean of...
John knows that monthly demand for his product follows a normal distribution with a mean of 2,500 units and a standard deviation of 425 units. Given this, please provide the following answers for John. a. What is the probability that in a given month demand is less than 3,000 units? b. What is the probability that in a given month demand is greater than 2,200 units? c. What is the probability that in a given month demand is between 2,200...
A manufacturer claims that the average mileage of his automobiles is at least 25mpg. In a...
A manufacturer claims that the average mileage of his automobiles is at least 25mpg. In a previous study it was found that the standard deviation of the mileage of his automobiles is 3mpg. For a .05 level of significance, what sample size would be recommended if the researcher wants an 80% chance of detecting that is less than 25 miles per gallon when it is actually 24 (to the next whole number)? A. 71 B. 95 C. 56 D. 28
A local drugstore owner knows that, on average, 100 people enter his store each hour. Find...
A local drugstore owner knows that, on average, 100 people enter his store each hour. Find the probability that in a given 3-minute period nobody enters the store. Show work below. Find the probability that in a given 3-minute period more than 5 people enter the store. Show work below.
a) (i). A manufacturer of metal pistons finds that on the average, 12% of his pistons...
a) (i). A manufacturer of metal pistons finds that on the average, 12% of his pistons are rejected because they are either oversize or undersize. What is the probability that a batch of 10 pistons will have not more than 2 rejections? (ii). A company makes electric motors. The probability an electric motor is defective is 0.01. What is the probability that a sample of 300 electric motors will contain exactly 5 defective motors? Q4(b) (i). The time in hours,...
A menswear manufacturer knows that the height of all men is normal with a mean of...
A menswear manufacturer knows that the height of all men is normal with a mean of 69 inches and a standard deviation of 3 inches. a) What proportion of all men have a height between 69 and 74 inches? b) What proportion of all men have a height between 67 and 74 inches? c) What is the 95th (and 99th) percentile of all men’s heights?
A manufacturer knows that their items have a lengths that are skewed right, with a mean...
A manufacturer knows that their items have a lengths that are skewed right, with a mean of 18.5 inches, and standard deviation of 3.9 inches. If 36 items are chosen at random, what is the probability that their mean length is greater than 16.8 inches? (Round answer to four decimal places)
A manufacturer knows that their items have a lengths that are skewed right, with a mean...
A manufacturer knows that their items have a lengths that are skewed right, with a mean of 10.6 inches, and standard deviation of 3.3 inches. If 46 items are chosen at random, what is the probability that their mean length is greater than 11.2 inches? (Round answer to four decimal places)
A manufacturer knows that their items have a lengths that are skewed right, with a mean...
A manufacturer knows that their items have a lengths that are skewed right, with a mean of 14.2 inches, and standard deviation of 4.4 inches. If 45 items are chosen at random, what is the probability that their mean length is greater than 12.7 inches?
A.) A manufacturer knows that their items have a normally distributed lifespan, with a mean of...
A.) A manufacturer knows that their items have a normally distributed lifespan, with a mean of 6.9 years, and standard deviation of 1 years. If you randomly purchase one item, what is the probability it will last longer than 9 years? B.) A particular fruit's weights are normally distributed, with a mean of 784 grams and a standard deviation of 24 grams. If you pick one fruit at random, what is the probability that it will weigh between 845 grams...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT