Question

Suppose that the high temperature on an August day in Death Valley varies between 98 and 118 degrees Fahrenheit and is uniformly distributed over this range of values. g There is a _____% chance that the high temperature will exceed 100 degrees on an August day. Please give your answer as percent, rounded to the nearest whole percent (e.g. 5, 72).

Answer 1

There is a 10% chance that the high temperature will exceed 100 degrees on an August day.

Explanation:

A distribution is called uniform if each outcome has the same probability of happening.

The uniform distribution has two bounds, a and b, and the probability of finding a value higher than x is given by:

`P(X > x) = (b - x)/(b - a)`

Suppose that the high temperature on an August day in Death Valley varies between 98 and 118 degrees Fahrenheit and is uniformly distributed over this range of values.

This means that
`a = 98, b = 118`

Probability that it exceeds 100 degrees:

`P(X > 100) = (100 - 98)/(118 - 98) = 0.1`

0.1*100% = 10%.

There is a 10% chance that the high temperature will exceed 100 degrees on an August day.