Problem

The number of chocolate chips in an 18-ounce bag of Chips Ahoy! chocolate chip cookies is approximately normally distributed, with a mean of 1262 chips and a standard deviation of 118 chips, according to a study by cadets of the U.S. Air Force Academy. The interquartile range of the number of chips in Chips Ahoy! cookies is chocolate chips. (Round to the nearest whole number as needed.)

Solution

Step 1 :The problem states that the number of chocolate chips in an 18-ounce bag of Chips Ahoy! chocolate chip cookies is approximately normally distributed, with a mean of 1262 chips and a standard deviation of 118 chips.

Step 2 :The interquartile range (IQR) is a measure of statistical dispersion, being equal to the difference between the upper and lower quartiles. In a normal distribution, the first quartile (Q1) is approximately 0.675 standard deviations below the mean, and the third quartile (Q3) is approximately 0.675 standard deviations above the mean.

Step 3 :Therefore, the IQR can be calculated as follows: \(IQR = Q3 - Q1 = (mean + 0.675*std_dev) - (mean - 0.675*std_dev) = 2*0.675*std_dev\)

Step 4 :We can substitute the given mean and standard deviation into this formula to find the IQR. mean = 1262, std_dev = 118, IQR = 159.3

Step 5 :Round the IQR to the nearest whole number, we get \(round(IQR) = 159\)

Step 6 :Final Answer: The interquartile range of the number of chips in Chips Ahoy! cookies is approximately \(\boxed{159}\) chocolate chips.

From Solvely APP
Source: https://solvelyapp.com/problems/20210/

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