Question

In: Statistics and Probability

A local produce supplier has determined that 5% of its orders are sent out with items...

A local produce supplier has determined that 5% of its orders are sent out with items missing due to the availability of the produce. This week the supplier filled 340 orders. What is the probability that fewer than 10 were sent out incomplete?

Multiple Choice

A.0409

B.2296

C.0818

D.4591

Expert Solution

Answer: Option A

The probability of an order being incomplete = 0.05 = p (say)

The total number of orders sent = 340 = n (say)

Let X be a random variable denoting the number of orders that are incomplete.

So

where n is the total number of trials and p is the probability of the occurrence of the event. (Here the event is: order sent is incomplete)

Now since n is >=30 ,it means that we can approximate this binomial distribution as normal distribution.

Normal approximation for a binomial distribution has mean = np and variance = np(1-p)

The curve represents the normal distribution given by the aforementioned equation.

The shaded region is the required probability as it represents P(X<10)

orchestra answered 1 year ago

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