Homework Help: Normal Distrubution Question

1. Dec 23, 2008

thomas49th

1. The problem statement, all variables and given/known data
From expirence a higher jumper knows he can claer a height of at least 1.78m once in 5 attempts. He also knows that he can clear a height of at least 1.65m on 7 out of 10 attempts

Assuming that the heights the high jumper can reach follow a Normal Distribution,

a) Draw a sketch to illustrate the information above

b) find, to 3 decimal places, the mean and the standard deviation of the heights the higher-jumper can reach

c) Calculate the probability that he can jump atleast 1.74m

2. Relevant equations

You'll need the distribution table

3. The attempt at a solution
Part a)

Well I can form the equations

P(h >= 1.78) =0.2
P(h >= 1.65) = 0.7

so what we're saying is the probability the height will be atleast 1.78m is 0.2
and
so what we're saying is the probability the height will be atleast 1.65m is 0.7

okay

so how do i go about drawing these on a normal distrubution. I think I have to do the flip around thing but im not sure why?

Thanks :)

2. Dec 23, 2008

HallsofIvy

First thing you need to do is find the z values from a table of the standard normal distribution corresponding to P(z)= 0.2 and P(z)= 0.7. I'll call those z0.2 and z0.7.
Here's a good table: http://www.itl.nist.gov/div898/handbook/eda/section3/eda3671.htm

The formula for changing from a normal distribution with mean $\mu$ and standard deviation $\sigma$ is $z= (x-\mu)/\sqrt{\sigma}$. Solve $z_{0.2}= (1.64- \mu)/\sqrt{\sigma}$ and $z_{0.7}= (1.78- \mu)/\sqrt{z}$ for $\mu$ and $\sigma$.

Use that information to draw the appropriate "bell shaped curve" with correct mean and standard deviation and to find $P(h\ge 1.74)$.

3. Dec 23, 2008

thomas49th

Ahh yes, I know about the standardising using the formula, ill need that for part B

so P(z) = 0.2

z = 0.07926

P(z) = 0.7
z = 1 - phi(0.7)
= 1 - 0.11791
= 0.8209

Is that right?

Thanks :)