Medical treatment will cure about 87% of all people who suffer from a certain eye disorder. Suppose a large medical clinic treats 57 people with this disorder. Let r be a random variable that represents the number of people that will recover. The clinic wants a probability distribution for r.

a. Estimate P(r is less than or equals 47)

b. Estimate P(47 is less than or equal to r that is less than or equal to 55)

Given that x is a normal variable with mean =110 and standard deviation of 12, find:

a. Find z such that 25% of the area under the standard normal curve lies to the right of z.

b. Find z such that 15% of the area under the standard normal curve lies to the right of z.

c. Find z such that 40% of the area under the standard normal curve lies between z and -z.