25% of the students don’t do the homework if it will not be graded. Suppose ther

Question

25% of the students don’t do the homework if it will not be graded. Suppose there are 45 students in this class.   Use Normal approximation to Binomial to answer the next 4 questions (check your answers using BINOMDIST function):

Can you apply the Normal approximation to this Binomial problem?

What is the mean of the normal distribution?   The standard deviation?  

Find the probability of 15 students not doing the HW.

Find the probability that between 10 and 30 students will not do the homework.

Explanation / Answer

a.
Normal Approximation to Binomial Distribution
Mean ( np ) =45 * 0.25 = 11.25
Standard Deviation ( npq )= 45*0.25*0.75 = 2.9047
Normal Distribution = Z= X- u / sd                   

b.
P( X = 15 ) = ( 45 15 ) * ( 0.25^15) * ( 1 - 0.25 )^30
= 0.0574
c.
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 10) = (10-11.25)/2.9047
= -1.25/2.9047 = -0.4303
= P ( Z <-0.4303) From Standard Normal Table
= 0.33348
P(X < 30) = (30-11.25)/2.9047
= 18.75/2.9047 = 6.4551
= P ( Z <6.4551) From Standard Normal Table
= 1
P(10 < X < 30) = 1-0.33348 = 0.6665                  

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