2 simple Normal Distribution and Empirical Rule problems. Please help!

1) A normal distribution has a mean of 50 and a standard deviation of 6. What is the probability that a value selected at random from this data is in the interval from 44 to 50?

2) A local bakery makes wheat bread. The number of grains of wheat in the bread is normally distributed, with a mean of 11.4g and a standard deviation of 1.3g. If this bakery sells 100 loaves of bread, approximately how many of the loaves (rounded to the nearest loaf) had less than 8.8g of wheat grains?

Please help me with these, I'm so stumped.

iryna said:

1) A normal distribution has a mean of 50 and a standard deviation of 6. What is the probability that a value selected at random from this data is in the interval from 44 to 50?

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Hint: The mean is 50, and one standard deviation less is 50 - 6 = 44. What percentage of the values in any standard normal distribution must fall within this interval?

iryna said:

2) A local bakery makes wheat bread. The number of grains of wheat in the bread is normally distributed, with a mean of 11.4g and a standard deviation of 1.3g. If this bakery sells 100 loaves of bread, approximately how many of the loaves (rounded to the nearest loaf) had less than 8.8g of wheat grains?

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What is the mean? What is two deviations less than the mean? What percentage of the values must be less than two deviations less than the mean?

Since you titled this "Empirical Rule" problems, and each of these has values that are an integer multiple of the standard deviation from the mean, stapel is suggesting you use the "empirical rule" so that you do not have to look the values up in a table. More generally, and as a check here, you can use the fact that the "standard" normal distribution \(\displaystyle z= \frac{x- \mu}{\sigma}\), where \(\displaystyle \mu\) is the mean and \(\displaystyle \sigma\) is the standard deviation, and look up the values in a table of the standard normal distribution. A good one is at http://www.math.bgu.ac.il/~ngur/Teaching/probability/normal.pdf.