In a local university, 40% of the students live in dormitories. a random sample of n = 80 students is selected for a particular study.
(a) what is the sampling distribution of p? provide its general shape, its standard deviation, and its mean.
(b) what is the probability that the sample proportion (the proportion living in the dormitories) is between 0.30 and 0.50?

a) p is normally distributed with mean P = 0.4 and standard deviation

δ = 0.05477

b) P( 0.3 < p < 0.5) = 0.9312

Step-by-step explanation:

a) What is the sampling distributión of P?

    p(sample proportion) is normally distributed with mean P and standard  

    deviation δ =

    how P = 0.40  population proportion of the students live in dormitories,        

    then p is normally distributed with mean P = 0.4 and standard deviation

     δ =

     δ = 0.05477

b) P( 0.3 < p < 0.5)

    Standardizing

    z = (p - P)/δ

                    = -1.82

                    = 1.82

     P(-1.82 < z < 1.82) = P(z < 1.82) - P(z<-1.82)

                                   =0.9656 - 0.0344

     P(-1.82 < z < 1.82) =  0.9312  

step-by-step explanation:

this woman was an important writer and propagandist during the american revolution. she was a member of the committee of correspondence (in fact the committee was formed in her home) and was an advisor to many of the revolutionary leaders, including george washington and john adams. who was this revolutionary woman?

the mean and mad

step-by-step explanation: