4) A medical treatment will cure about 87% of all people who suffer from a certa

Question

4) A medical treatment will cure about 87% of all people who suffer from a certain eye disorder. Suppose a large Medical elinic treats 57 people with this disorder. a.) Estimate the probability that no more than 47 people are cured. b.) Estimate the probability that between 47 and 55 people are cured (including 47 and 55) 5.) The manu facturer of a new car claims that miles per gallon for the gas consumption is normally distributed with a mean of 25.9 mpg and a standard deviation of 3.1 mpg. a) If one car is tested, what is the probability that the mean mpg is less than 24 mpg b.) If 30 ea c.) If one car is tested, what is the probability that the mean mpg is between 24 and 27 d.) If 30 cars tested, what is the probability that the mean mpg is less than 24 mpg? rs are mpg? tested, what is the probability that the mean mpg for all 30 cars is between 24 and 27 mpg? are

Explanation / Answer

4) here mean =np =57*0.87=49.59

and std deviation =(np(1-p))1/2 =2.539

a)as we know that from normal distribution z score =(X-mean)/std deviaiton

probability that no more then 47 people are cured=P(X<=47)=P(Z<(47.5-49.59)/2.539)=P(Z<-0.8231)=0.2052

b) P(47<=X<=55)=P((46.5-49.59)/2.539<Z<(55.5-49.59)/2.539)=P(-1.2170<Z<2.3277)=0.9900-0.1118=0.8782

5)

a) P(X<24)=P(Z<(24-25.9)/3.1)=P(Z<-0.6129)=0.2700

b) here std error of mean =std deviaiton/(n)1/2 =0.566

hence P(Xbar<24)=P(Z<(24-25.9)/0.566)=P(Z<-3.357)=0.0004

c)

P(24<X<27)=P(-0.6129<Z<0.3548)=0.6387-0.2700=0.3687

d)

P(24<Xbar<27)=P(-3.3570<Z<1.9435)=0.9740-0.0004 =0.9736

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