# A grocery store receives deliveries of corn from two farms, one in Iowa and the other in Ohio. Both farms produce ears of corn with mean weight 1.26 pounds. The standard deviation of the weights of the ears of corn from the farm in Ohio is 0.01 pound greater than that from the farm in Iowa. A randomly selected ear of corn from the farm in Iowa weighed 1.39 pounds, which has a standardized score of 1.645 for the distribution of weights for the Iowa corn. If an ear of corn from the farm in Ohio weighs 1.39 pounds, how many standard deviations from the mean is the weight with respect to the Ohio distribution

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## Question:

A grocery store receives deliveries of corn from two farms, one in Iowa and the other in Ohio. Both farms produce ears of corn with mean weight 1.26 pounds. The standard deviation of the weights of the ears of corn from the farm in Ohio is 0.01 pound greater than that from the farm in Iowa. A randomly selected ear of corn from the farm in Iowa weighed 1.39 pounds, which has a standardized score of 1.645 for the distribution of weights for the Iowa corn. If an ear of corn from the farm in Ohio weighs 1.39 pounds, how many standard deviations from the mean is the weight with respect to the Ohio distribution

Using the normal distribution, it is found that the weight with respect to the Ohio distribution is 1.46 standard deviations from the mean.

In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:

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• It measures how many standard deviations the measure is from the mean.
• After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

For the Iowa farm:

• The mean is of 1.26 pounds, hence .
• The weight is of 1.39 pounds, hence
• The standardized score is of 1.645, hence .

Then, the standard deviation can be found as follows:

In Ohio:

• Same mean.
• Standard deviation 0.01 pound greater, hence
• Same weight.

Hence:

The weight with respect to the Ohio distribution is 1.46 standard deviations from the mean.

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