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

Answer:

84%.

Step-by-step 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

$x = 48$.

$\displaystyle z = \frac{x - \mu}{\sigma} = \frac{48 - 40}{8} = 1$.

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

In other words,

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