The numbers of cookies in a shipment of bags are normally distributed, with a mean of 64 and a standard deviation of 4. what percent of bags of cookies will contain between 64 and 68 cookies?

We are provided that the number of cookies in a shipment bag are normally distributed with mean equal to 64 and standard deviation equal to 4.

We want to find the percentage of cookies between 64 and 68. Note that 64 is the mean and 68 is 1 standard deviation above the mean as 64 + 4 = 68.

Since, the number of cookies is normally distributed, we can use the Empirical Rule to approximate the percentage of cookies between the given end points.

According to the empirical rule, 68% of the data values lie within 1 standard deviation from the mean. This means going from 1 standard deviation below to mean to 1 standard deviation above the mean we cover 68% of the data values.

Since normal distribution is symmetric about the mean, we can say that from these 68% half of the value lies 1 standard deviation below the mean and rest half lie 1 standard deviation above the mean. Half of 68% if 34%, so we can say 34% of the value lie between the mean and 1 standard deviation above the mean.

Therefore, the answer to this question is: 34% bags of cookies will contain between 64 and 68 cookies.

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