# Thread: Solving problem involving normal distributions

1. ## Solving problem involving normal distributions

Asiah found that the time taken to travel from her house to her office is normally distributed with a mean of 40 minutes and a varience of 64 minutes^2.If she leaves home at 7:30am,Find the probability that she will arrive after 8:15 am

2. Transform it to the standard $\displaystyle Z$ distribution and look it up on your normal probability tables...

3. Originally Posted by mastermin346
Asiah found that the time taken to travel from her house to her office is normally distributed with a mean of 40 minutes and a varience of 64 minutes^2.If she leaves home at 7:30am,Find the probability that she will arrive after 8:15 am

$\displaystyle \sigma^2=64\Rightarrow\sigma=+\sqrt{64}=8\;\text{\ footnotesize\ minutes}$

You want the probability that the time taken is >45 minutes...

therefore, you require

$\displaystyle P\left(Z>\frac{x-\mu}{\sigma}\Rightarrow\ Z>\frac{45-40}{8}\right)$

In standard sports of a school,all students took part in the 100m race.The time taken to finish the race by a Form 2 student in normally distributed with a mean of 15 seconds and variance of 25 seconds^2.For a student who took less than 16 seconds,1 mark was awarded and for one who took less than 14 seconds,2 marks were awarded.

a)find the percentage of Form 2 students who got 1 mark each.

b)Find the number of Form 2 students who got 2 marks if 200 Form 2 students took part.

5. Originally Posted by mastermin346

In standard sports of a school,all students took part in the 100m race.The time taken to finish the race by a Form 2 student in normally distributed with a mean of 15 seconds and variance of 25 seconds^2.For a student who took less than 16 seconds,1 mark was awarded and for one who took less than 14 seconds,2 marks were awarded.

a)find the percentage of Form 2 students who got 1 mark each.

b)Find the number of Form 2 students who got 2 marks if 200 Form 2 students took part.
(a)

Again, the question gives the variance, so the standard deviation is the square root of that...

$\displaystyle \sigma=+\sqrt{25}=5$

$\displaystyle \mu=15$

$\displaystyle Z=\displaystyle\frac{x-\mu}{\sigma}=\frac{16-15}{5}=0.2$

Therefore, you need to find

$\displaystyle P(Z<0.2)$

The percentage of students who got one mark is then 100 times the probability
of a student finishing the race in less than 16 seconds.

Try that and then maybe (b) is do-able.