Solving problem involving normal distributions

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Aug 25th 2010, 06:38 AM
mastermin346

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

please help
Aug 25th 2010, 06:41 AM
Prove It

Transform it to the standard $Z$ distribution and look it up on your normal probability tables...
Aug 25th 2010, 06:48 AM
Archie Meade

Quote:

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

please help

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

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

therefore, you require

$P\left(Z>\frac{x-\mu}{\sigma}\Rightarrow\ Z>\frac{45-40}{8}\right)$
Aug 25th 2010, 07:10 AM
mastermin346

thanks archie meade

how about this..
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.
Aug 25th 2010, 08:09 AM
Archie Meade

Quote:

Originally Posted by mastermin346

thanks archie meade

how about this..
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...

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

$\mu=15$

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

Therefore, you need to find

$P(Z<0.2)$

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.