Dartmouth Distribution Warehouse makes deliveries of a large number of products to its customers. It is known that 78% of all the orders it receives from its customers are delivered on time. Let o be the proportion of orders in a random sample of 100 that are delivered on time. Find the probability that the value of P will be less than 0.81

The probability that the value of P will be less than 0.81 is 0.7642.

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

The standard deviation of this sampling distribution of sample proportion is:

Given:

n = 100

p = 0.78

Since n = 100 > 30, according to the central limit theorem the sampling distribution of sample proportion follows a Normal distribution.

Compute the value of as follows:

*Use a z-table for the probability.

Thus, the probability that the value of P will be less than 0.81 is 0.7642.

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step-by-step explanation: