Question

Every now and then even a good diamond cutter has a problem and the diamond breaks. For one cutter, the rate of breaks is .2%. Suppose now that you want to find the probability that at least 1 is broken when twelve diamond cutters are selected at random. Choose the option below that best answers how to do this question. Let X be the discrete random variable that represents the number of breaks. Assume a binomial distribution.

a. do (.998)^12 Ob)
b. do 1 – [(-998)^12] c)
c. calculate P(X=1) + P(X=2) +...+ P(X=12) using the binomial formula or an individual table in excel d)
d. calculate the P(X31) using the binomial formula or a cumulative table in excel e)
e. both b and care correct f)
f. both c and d are correct

Answer 1

calculate P(X=1) + P(X=2) +...+ P(X=12) using the binomial formula or an individual table in excel

calculate the P(X ≥ 12) using the binomial formula or a cumulative table in excel

Explanation:

For a binomial distribution :

P(x =x) = nCx * p^x * (1 - p)^(n - x)

n = number of trials = 12 ; x = number of successes

p = probability of success = 0.2% = 0.002

1 - p = 1 - 0.002 = 0.998

Probability that atleast 1 is broken ;

p(1) + p(2) + p(3) +... + p(12) ;

This can be calculated by summing the values obtained using the binomial formula or in excel.

Alternatively, using the binomial formular or excel, the cumulative probability could be obtained as P(x ≥ 1)