I need a calculated solution regarding the following question: CDs are produced
ID: 3332390 • Letter: I
Question
I need a calculated solution regarding the following question:
CDs are produced by a firm. The number of flaws, X, on a CD has the following probability distribution:
1. Calculate the mean and standard deviation of the number of flaws per CD and describe the distribution of the average number of flaws per CD in a sample of 400 CDs. Calculate the mean and variance of this distribution.
2. what is the probability that the mean number of flaws per CD in a batch of 400 is less than 0.3?
X p(x) 0 0.75 1 0.15 2 0.10Explanation / Answer
1. Mean = xp(x)
= 0*0.75 + 1*0.15 + 2*0.10
= 0.35
Variance 2 = x2p(x) - Mean2
= 0*0.75 + 1*0.15 + 4*0.10 - 0.35*0.35
= 0.4275
Standard deviation = 0.4275 = 0.6538.
Since the probabilities sum to 1, the average number of flaws form a normal distribution.
Sample variance s2 = 2 / n
= 0.4275 / 400
= 0.00106875
2. Sample standard deviation s = 0.00106875 = 0.03269
x = + zs
=> 0.3 = 0.35 + 0.03269z
z = (0.3 - 0.35) / 0.03269
= -1.5295
Probability from tables = 0.0631.
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