at a small coffee shop, the distribution of the number of seconds it takes for a cashier to process an order is approximately normal with mean 276 seconds and standard deviation 38 seconds. which of the following is closest to the proportion of orders that are processed in less than 240 seconds?

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MrRoyalid MrRoyalid · Answer 1

The closest to the proportion of orders that are processed in less than 240 seconds is 17%

From the question, the given parameters about the distribution are

The z-score of the data value is calculated using the following formula

z = (x - mean value)/standard deviation

Substitute the known values in the above equation, so, we have the following representation

z = (240- 276)/38

Evaluate

z = -0.95

The closest proportion is then calculated as:

P(x < 240) = P(z < -0.95)

From the z table of probabilities, we have;

P(x < 240) = 0.17106

This gives

P(x < 240) = 17.106%

Approximate

P(x < 240) = 17%

Hence, the closest proportion is 17%