1) A Motor Company has purchased steel parts from a supplier for several years and has found that 10% of the parts must be returned because they are defective. An order of 25 parts is received. What are the mean and standard deviation of the defective parts?
A) Mean = 3.5; standard deviation = 2.5
B) Mean = 2.5; standard deviation = 1.5
C) Mean = 1.5; standard deviation = 2.5
D) Mean = 2.5; standard deviation = 3.5
2)Given a binomial random variable with n = 15 and = 0.4, find the following probability using the binomial table. P (6 < x < 10)
A) 0.0338
B) 0.1181
C) 0.0947
D) 0.3564
For 1).
Your values are the following:
p = .1, q = 1 - p = .9, and n = 25
To find mean and standard deviation:
mean = np = (25)(.1) = ?
standard deviation = √npq = √(25)(.1)(.9)= ?
I'll let you finish the calculations to answer the question.
For 2).
Use the binomial table to determine your answer for the values given.
I hope this will help get you started.
1) To find the mean and standard deviation of defective parts, we need to use the concept of a binomial distribution. In a binomial distribution, we have two possible outcomes: defective or not defective.
The mean of a binomial distribution is given by the formula μ = np, where n is the number of trials (in this case, the number of parts received) and p is the probability of success (in this case, the probability of a part being defective).
In this case, we know that 10% of the parts must be returned because they are defective, so the probability of a part being defective is 0.10. The number of parts received is 25.
Therefore, the mean μ = (25)(0.10) = 2.5
The standard deviation of a binomial distribution is given by the formula σ = sqrt(np(1-p)).
Using the same values, we can calculate the standard deviation σ = sqrt((25)(0.10)(1-0.10)) = 1.5
Therefore, the correct answer is B) Mean = 2.5; standard deviation = 1.5.
2) To find the probability P(6 < x < 10), we need to use the binomial table.
The binomial table provides the cumulative probabilities for different values of x (the number of successes) in a binomial distribution.
In this case, we have a binomial distribution with n = 15 (number of trials) and p = 0.4 (probability of success).
To find P(6 < x < 10), we need to calculate the cumulative probability for x = 6 and subtract the cumulative probability for x = 10 from it.
Using the binomial table, we can look up the cumulative probabilities for x = 6 and x = 10.
Let's say the cumulative probability for x = 6 is 0.4506 and the cumulative probability for x = 10 is 0.5865.
Now, to find P(6 < x < 10), we subtract the cumulative probability for x = 10 from the cumulative probability for x = 6.
P(6 < x < 10) = 0.5865 - 0.4506 = 0.1359
Therefore, the correct answer is not among the options given.