a company receives a large shipment of computer monitors the

a company receives a large shipment of computer monitors. the company will accept or reject the shipment based on a arrandom sample of twenty monitors from the shipment. Each monitor is tested for defects or substandard performance. Let Y be the number of monitors, in the sample, that are found to be defective or to have substandard performance. Suppose that the company will reject the shipment if Y >= 3. Assume that the probability that a given monitor is found to be defective or to have substandard performance is p =.05

a) Find the mean and standard deviation of Y.

b) Find the probability that the shipment will be accepted. Round to 4 decimal places.

Solution

A)

As

mean = n p = 20*0.05 = 1 [ANSWER]

standard deviation = sqrt(np(1-p)) = sqrt(20*0.05*(1-0.05)) = 0.974679434 [ANSWER]

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b)

The number of defects must be at most 2.

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    20      
p = the probability of a success =    0.05      
x = the maximum number of successes =    2      
          
Then the cumulative probability is          
          
P(at most   2   ) =    0.924516326 [ANSWER]