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A highway department has enough salt to handle a total of 80 inches of snowfall. Suppose the daily amount of snow has a mean of 1.5 inches and a standard deviation of 0.3 inches. What can be inferred about the salt supply?

A) It will last for 50 days
B) It will last for 60 days
C) It will last for 40 days
D) It will last for 55 days

1 Answer

3 votes

Final answer:

The salt supply will last for 263 days.

Step-by-step explanation:

To determine how long the salt supply will last, we need to calculate the number of days it would take for the cumulative snowfall to reach 80 inches. Since the daily amount of snow has a mean of 1.5 inches and a standard deviation of 0.3 inches, we can use the normal distribution to estimate the number of days it would take for the cumulative snowfall to reach a particular value. The formula to calculate the number of days is N = (X - mean) / standard deviation, where N is the number of days, X is the desired total snowfall, and mean is the mean daily snowfall. So, N = (80 - 1.5) / 0.3 = 262.5. Since we can't have a fractional number of days, we round up to the nearest whole number. Therefore, the salt supply will last for 263 days, which is option E) None of the above.

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