Question

The time that a skier takes on a downhill course has a normal distribution with a mean of12.3 minutes and standard deviation of 0.4 minutes.
The probability that on a random run the skier takes between 12.1 and 12.5 minutes is ____.

a) 0.1915 b) 0.383 c) 0.3085 d) 0.617

Answer 1

Answer:

Option b

Step-by-step explanation:

Given that the time that a skier takes on a downhill course has a normal distribution with a mean of 12.3 minutes and standard deviation of 0.4 minutes.

If X is the time that the skier takes then

X is N(12.3,0.4)

To convert this to Z score we can use the following

$z=\frac{x-12.3}{0.4}$

The probability that on a random run the skier takes between 12.1 and 12.5 minutes

=$P(12.1<X<12.5)\\= P(|x-12.3|<0.2)\\=P(|z|<0.5)$

=0.383

Option b is right.