[MATH SL]Statistics Help

[1-2-3]

I need help with this Normal Distribution question:

The heights of boys at a particular school follow a normal distribution with a standard

deviation of 5 cm . The probability of a boy being shorter than 153 cm is 0.705.

a) Calculate the mean height of the boys.

b) Find the probability of a boy being taller than 156 cm .

What I did is:

a) ((153 - Mean)/5) = 0.705

Mean = 149 cm

b) P (X <156)

= 1 - P(X </= 156)

Using the GDC,

1 - normalcdf (-10^99, 156, 150, 5)

= 0.115

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What the answer says is:

(Look at the attached file)

What am I doing wrong ?

[moneyfaery]

a) You know that probability is calculated by P(Z < x-μ/σ)

μ=??

σ=5

x=153

Find μ:

P(Z < 153-μ/5) = 0.705 {this is given}

invNorm(0.705) = 0.5388 {gives value for Z}

invNorm(area[,μ,σ])

Therefore, Z < 153-μ/5 = 0.5388 and solve for μ to get 150

Bad notation, I know, but extra brackets looked ugly.

b) Find P(X >156):

You can just use the lowerbounds, upperbounds, and values for μ and σ in this case

normalcdf(156,1EE99,150.3,5) = 0.127

normalcdf(lowerbound,upperbound[,μ,σ])

If you don't enter the values for [,μ,σ], you'll be calculating the values of the Z-index by default.

Edited May 4, 2009 by Irene

[lois lee]

hey,

i was wondering if that question would be on a higher paper or on a standard paper. i am doing higher and just cant get to grips with maths yet!

thanks

lo