1. Find the area under the normal curve which is shaded on the graph. Use 4 decimal places.
2. For a standard normal distribution, find the percentage of datathat are more than 1 standard deviationaway from the mean. Use two decimal places. For example, 12.34% should be written as 12.34
3. The Precision Scientific Instrument Company manufactures thermometers which are supposed to give readings of 0o C at the freezing point of water. Tests on a large sample of these thermometers reveal that at the freezing point of water, some give readings below 0o C (denoted by negative numbers) and some give readings above 0o C (denoted by positive numbers). Assume that the mean reading is 0o C and the standard deviation of the readings is 1o C. Also assume that the frequency distributionof errors closely resembles the normal distribution. If 9% of the thermometers are rejected because they have readings that are too high, but all other thermometers are acceptable, find the temperature that separates the rejected thermometers from the others. Use two decimal places. Do not use any words or the degree symbol in your answer.
4. The amount of snowfall falling in a certain mountain rangeis normally distributed with a mean of 89 and a standard deviation of 16 inches. What is the probabilitythat the mean annual snowfall during 64 randomly picked years will exceed 91.8 inches? Use 4 decimal places.
5. An airline experiences a no-show rate of 6%. What is the maximum number of reservations that it could accept for a flight with a capacity of 160, if it wants the probability of accommodating all reservation holders to be at least 95%.
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The solution solves for the different probabilities in the given question using EXCEL functions. The standard distribution tables are not needed to solve the questions below. All the answers are calculated using built-in Excel formulas.