Question

The times recorded for a group of students completing a physical obstacle course are normally distributed with a mean time of 25 minutes and a standard deviation of 5 minutes. Using the normal curve distribution shown, find the percentage of students that completed the obstacle course between 20 and 35 minutes.​

Answer 1

0.8180

Explanation:

Given:

μ = 25 minutes

τ = 5 minutes

x₁ = 20 minutes

x₂ = 35 minutes

`\boxed{Z=(x-\mu)/(\tau) }`

`Z_1=(x_1-\mu)/(\tau)`

`=(20-25)/(5)`

`=-1`

`Z_2=(x_2-\mu)/(\tau)`

`=(35-25)/(5)`

`=2`

P(-1≤Z≤2) = P(Z=2) - P(Z=-1)

= 0.8415 - 0.0235

= 0.8180