Mathematics > STUDY GUIDE > MATH 225N Week 5 Assignment: Applications of the Normal Distribution – Excel (2020) solution guide (All)

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MATH 225N Week 5 Assignment: Applications of the Normal Distribution – Excel (2020) solution guide

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Sugar canes have lengths, X, that are normally distributed with mean 365.45 centimeters and standard deviation 4.9 centimeters. What is the probability of the length of a randomly selected cane being between 360 and 370 centimeters?  Round your answer to four decimal places. The mean is μ=365.45, and the standard deviation is σ=4.9. As the probability between two values is to be calculated, subtract the probability of the lower value from the higher value. In this case, you have to use the NORMDIST function twice. 1. Open Excel and click on any empty cell. Click Insert function, fx. 2. Search for NORMDIST in the search for a function dialog box and click GO. 3. Make sure NORMDIST is on top in select a function. Then click OK. 4. In the function arguments of NORMDIST function, enter 370 for X, 365.45 for Mean, 4.9 for Standard_dev, and TRUE for Cumulative, all for the higher value of X. Thus, the answer, rounded to four decimal places, is 0.8234. 5. Click on any other empty cell. Click Insert function, fx. 6. Search for NORMDIST in the search for a function dialog box and click GO. 7. Make sure NORMDIST is on top in select a function. Then click OK. 8. In the function arguments of NORMDIST function, enter 360 for X, 365.45 for Mean, 4.9 for Standard_dev, and TRUE for Cumulative, all for the lower value of X. Thus, the answer, rounded to four decimal places, is 0.1330. Now subtract, 0.8234−0.1330=0.6904. Thus, the probability of the length of a randomly selected cane being between 360 and 370 centimeters is 0.6904. Suppose that the weight of navel oranges is normally distributed with a mean of μ=6 ounces and a standard deviation of σ=0.8 ounces. Find the weight below that one can find the lightest 90% of all navel oranges.  Use Excel, and round your answer to two decimal places. The weights of bags of raisins are normally distributed with a mean of 175 grams and a standard deviation of 11 grams. Bags in the upper 4.5% are too heavy and must be repackaged. Also, bags in the lower 5% do not meet the minimum weight requirement and must be repackaged. What are the ranges of weights for raisin bags that need to be repackaged?  Use Excel, and round your answers to the nearest integer. The time, X minutes, taken by Tim to install a satellite dish is assumed to be a normal random variable with mean 127 and standard deviation 20. Determine the probability that Tim will takes less than 150 minutes to install a satellite dish.  Round your answer to four decimal places.

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