Question

Students who take statistics courses have a normal distribution period of 55 minutes on average and 15 minutes of standard deviation. Find the probability that any student spends 65-85 minutes on the exam.

Answer 1

Solution-

According to question, students who take statistics courses have a normal distribution period of 55 minutes on average and 15 minutes of standard deviation.

So, mean = $\mu$ = 55 minutes

And Standard deviation = $\sigma$ = 15 minutes.

If the random normal variable is X.Then

The probability that any student spends 65-85 minutes

= P( 65 < X < 85)

65 85- = P <

$=P\left ( \frac{65-55}{15}<z<\frac{85-55}{15} \right )$

10 30 = P 2 15 15

$=P\left ( 0.667<z<2 \right )$

$=P\left ( 0<z<2 \right )-P(0<z<0.667)$

= 0.4772 - 0.2486

= 0.2286

(Values are taken from standard normal distribution table).

Hence, Probability that any student spends 65 minutes to 85 minutes is 0.2286 .