a major pharmaceutical company has published data on effective dosages for their

Question

a major pharmaceutical company has published data on effective dosages for their new product, FeelWell. It recommends that patients be given the minimum effective dose of FeelWell and reports that the mean effective minimum dose is 250mg, with a standard deviation of 75mg . a.) assuming that dosage effectiveness is normally distributed, what level will be effective for all but 2% of the population? b.) what does level can be expected to be too low for all but approximately 2%? c.) what percentage of people should be okay with a minimum dosage of 325mg? d.) what percentage of people should take between 100 and 215mg?

Explanation / Answer

Given that mean = 250 , sd = 75

and z for all but 2% means that the area under the normal graph is = 1-0.02 = 0.98, we know that z= (x-mean)/sd

so 0.98*75 = x-250 =

x = 250+0.98*75= 323.5 , would be effective for 98%

b) here z = 0..02 , again using the same formula as above we get the

0.02*75 = x-250 =

x= 250+0.02*75=251.5

c) for x = 325 , we get

Z = 325-250/75 = 75/75 = 1

so we need to find p(z>1) , please keep the z tables handy for this

P ( Z>1 )=1P ( Z<1 )=10.8413=0.1587 , hence 15.875

d)

here we need to find

P(100<X<215) =

(100-250)/75 <Z < (215-250)/75

P(-2<Z<0.46)

To find the probability of P (2<Z<0.46), we use the following formula:

P (2<Z<0.46 )=P ( Z<0.46 )P (Z<2 )

We see that P ( Z<0.46 )=0.6772.

P ( Z<2 ) can be found by using the following fomula.

P ( Z<a)=1P ( Z<a )

After substituting a=2 we have:

P ( Z<2)=1P ( Z<2 )

We see that P ( Z<2 )=0.9772 so,

P ( Z<2)=1P ( Z<2 )=10.9772=0.0228

At the end we have:

P (2<Z<0.46 )=0.6544

hence the answer is 65.44%

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