The probability that a school bus is late is 0.04. How many times would you expect the bus to be late in a 5-week period?
That's 25 school days. The average or "expectation" number of late appearances will be 25x0.04 = 1.0, but there are non-zero probabilities of 0,2,3, etc. late appearances as well. The binomial distribution can be used to calculate their probabilities.
To determine the number of times we can expect the bus to be late in a 5-week period, we need to multiply the probability of the bus being late on any given day by the number of school days in a 5-week period.
First, let's calculate the number of school days in a 5-week period.
A week typically has 7 days, so a 5-week period would have 5 * 7 = 35 days.
Next, we need to multiply the probability of the bus being late on any given day by the number of school days.
Probability of the bus being late = 0.04
Expected number of late days = Probability of being late * Number of school days
Expected number of late days = 0.04 * 35
Expected number of late days = 1.4
Therefore, we can expect the bus to be late approximately 1.4 times in a 5-week period. Since it is not possible to have 0.4 of an occurrence, we can round it to 1 occurrence or say that the expected number of late days is 1.