Final answer:
To calculate the likelihood of sufficient salt for snowfall, the mean and standard deviation are used to estimate the total snowfall over 50 days.
Step-by-step explanation:
The student's question revolves around calculating the probability that the salt on hand will suffice for the next 50 days, given that the daily amount of snow has a mean of 1.5 inches and a standard deviation of 0.3 inches. In order to answer this, we will assume that the snowfall follows a normal distribution and apply the central limit theorem.
First, we calculate the mean snowfall over 50 days, which is 50 days * 1.5 inches/day = 75 inches. The standard deviation for the sum of 50 days of snowfall can be found by multiplying the daily standard deviation by the square root of the number of days: 0.3 inches * sqrt(50) days. This is because the standard deviations add up in quadrature when independent random variables are summed.
To determine the probability of the snowfall being 80 inches or less, we would calculate the z-score for 80 inches and then look up this score in a standard normal distribution table or use a calculator/software capable of such computation. However, based on the given information, it seems likely that the salt would suffice since the mean total snowfall over 50 days is below 80 inches.