A random sample of 10 resistors is to be tested From past ex

A random sample of 10 resistors is to be tested. From past experience, it is known that the probability of a given resistor being defective is 0.08. Let X be the number of defective resistors.

a. What kind of distribution function would be recommended for modeling X?

b. According to the distribution function in (a), what is the probability that in the sample of 10 resistors there are more than 1 defective resistors in the sample?

Solution

a)

A binomial distribution, as the trials are independent and the probability of success is constant. Also, there is a fixed number of trials.

b)

Note that P(more than x) = 1 - P(at most x).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    10      
p = the probability of a success =    0.08      
x = our critical value of successes =    1      
          
Then the cumulative probability of P(at most x) from a table/technology is          
          
P(at most   1   ) =    0.812117545
          
Thus, the probability of at least   2   successes is  
          
P(more than   1   ) =    0.187882455 [ANSWER]