A firm producing mugs has a quality control scheme in which a random sample of 10 mugs is taken from each batch is inspected. For 50 such samples, the numbers of defective mugs are as follows
Number of defective mugs 0 1 2 3 4 5 6+
Number of samples 5 13 15 12 4 1 0
i) find the mean and standard deviation of the number of deffective mugs per sample
ii) Show that a reasonable estimate for p, the probability that a mug is deffective, is 0.2. Use this figure to calculate the probability that a randomly chosen sample will contain exactly 2 deffective mugs. Comment on the agreement between this value and the observed date.
i have worked out the mean as 2 but i cant figure out how to do the others. Please help, sorry if its really simple of something but i really dont know how to work this out.
Answers & Comments
Verified answer
Stacey -
Yes, the mean = 2 so you are on the right track!
Now, the standard deviation is a little more complicated. First calculate the variance:
Step 1: sum the product of each x-value squared times the frequency:
0^2(5) + 1^2(13) + 2^2(15) + ... + 5^2(1) = 270
Step 2: Variance = Step 1 divided by N minus the mean squared:
Variance = 270/50 - 2^2 = 1.4
Now, the standard deviation = sqrt (1.4) = 1.1832
So, in summary, the mean = 2 and standard deviation = 1.1832
(ii) From your sample data, there were 2 x 50 = 100 defective mugs in total out of 50 x 10 = 500 mugs. So, on average, there are 100/500 = 0.20 defective mugs
So, if you randomly sampled 10 mugs, expect 0.20 x 10 = 2 defective mugs in the sample
Hope that helped