Question

The time required to finish a test in normally distributed with a mean of 40 minutes

and a standard deviation of 8 minutes. What is the probability that a student chosen
at random will finish the test in less than 48 minutes?
84%
2%
34%
16%

Answer 1

84%.

Explanation:

Let X be the time in minutes for a student chosen at random to finish the test.
`X\sim N(40, 8^(2))`.

The probability that a student chosen at random finishes the test in less than 48 minutes will represented as

`P(X< 48)`.

Method 1: technology

Evaluate the cumulative normal probability on a calculator, where

• The lower bound is 0,
• The upper bound is 48,
• The mean
  `\mu = 40`,
• The standard deviation
  `\sigma = 8`

`P(X < 48) = 0.8413`.

Method 2: z-score table

`x = 48`.

`\displaystyle z = (x - \mu)/(\sigma) = (48 - 40)/(8) = 1`.

Look up the entry that corresponds to
`z = 1.000` on a z-score table: 0.8413.

In other words,

`P(X < 48) = P(Z < 1) = 0.8413`.