Question

1.) A recent study indicated that 85% of all parents take candy from their child's trick-or-treat bag. If 30 parents are selected at random then what is the probability that 25 of them took Halloween candy from their child's trick-or-treat bag? Give your answer to four decimal places.

2.) Systolic blood pressure readings for females are normally distributed with a mean of 125 and a standard deviation of 10.34. If 60 females are randomly selected then find the probability that their mean systolic blood pressure is between 122 and 126. Give your answer to four decimal places.

3.) Apartment rental prices in Pittsburgh are approximately normally distributed with a mean of $838 and a standard deviation of $175. If a researcher wants to study people whose rent is in the lower 5% then find the maximum rent a person can pay and be part of the study. Give your answer to two decimal places and do not give units.

Answer 1

1)

Binomial Distribution:

P(X =r) =C(n, r).p^r.q^n-r

[P =Probability; C(n, r) =No. of ways of choosing r items from n items; r =required number of successes; n =Sample size; p =Probability of success on a single trial; q =1 - p].

P(X =25) =C(30, 25).(0.85)²⁵.(0.15)⁵ =0.1861

2)

Population mean, =125

Population standard deviation, =10.34

Sample mean =

Sample size, n =60

Z =(​​​​​​)/(​​​​​​)

At =122, Z =(122 - 125)/(10.34/​​​​​​) = -2.2474

At =126, Z =(126 - 125)/(10.34/​​​​​​) =0.7491

P(122 < < 126) =P(-2.2474 < Z < 0.7491) =0.7608

3)

At lower 5% of the data, the corresponding Z-score at maximum point of X is Z = -1.645

Z =(X - )/ X =Z + = -1.645(175) + 838 =550.12