The mean daily charge to a patient for medicines nursing car

The mean daily charge to a patient for medicines, nursing care and so no at the Sunny View Medical Center is $320 with the standard deviation of the distribution of charges of $25

a. What proportion of the patients are charged more that $350 per day?

b. What proportion of the patients are charged between $275 and $350 per day?

c. The president of Sunny View said that a profit was only being made on the upper 30% of the charges. Above what amount does the center make a profit?

Solution

let X be the random variable denoting the charge to a patient for medicines at sunny view medical center

given that X~N(320,25²)

a) P[X>350]=P[(X-320)/25>(350-320)/25]=P[Z>1.2]=1-P[Z<1.2]=1-0.884930=0.11507 [answer] where Z~N(0,1)

b) P[275<X<350]=P[(275-320)/25<Z<(350-320)/25]=P[Z<1.2]-P[Z<-1.8]=0.884930-0.0359303=0.8489997 [answer]

c)let the amount above which the center make profit be t

then P[X>t]=0.30 or, P[X<t]=0.70 or, P[Z<(t-320)/25]=0.70=P[Z<0.524401]

hence (t-320)/25=0.524401

hence t=$333.11 [answer]