A report indicates that 40 of the memory chips produced by c

A report indicates that 40% of the memory chips produced by certain manufacturer are defective. A computer store has received a shipment of 20 memory chips from the manufacturer.

a. What the probability that a least 5 of the chips in the shipment are defective?

b. What is the probability that majority of the chips in this shipment are no-defective?

c. What is the probability that the number of non-defective chips in this shipment is at least twice as many as the number of defective chips?

Solution

A)

Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    20      
p = the probability of a success =    0.4      
x = our critical value of successes =    5      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   4   ) =    0.050951953
          
Thus, the probability of at least   5   successes is  
          
P(at least   5   ) =    0.949048047 [ANSWER]

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b)

The probability that a chip is not defective is 1 - 0.40 = 0.60.

Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    20      
p = the probability of a success =    0.6      
x = our critical value of successes =    11      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   10   ) =    0.244662797
          
Thus, the probability of at least   11   successes is  
          
P(at least   11   ) =    0.755337203 [ANSWER]

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c)

This happens when at least 14 are non-defective.

           
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    20      
p = the probability of a success =    0.6      
x = our critical value of successes =    14      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   13   ) =    0.749989328
          
Thus, the probability of at least   14   successes is  
          
P(at least   14   ) =    0.250010672 [ANSWER]