Statistics and Probability Answers

Question 1.3 [4]

A set of eight cards contains one joker. Aviwe and Siphumlile are two players that are learning probability theory by playing card games with these 8 cards. Aviwe chooses 5 cards at random, Siphumlile takes the remaining three cards. What is the probability that Aviwe has the joker? Aviwe discards 4 cards and Siphumlile discards two cards. It is know that the joker has not been discarded, what is the probability that Aviwe has the joker? Explain your answer in detail.

Question 1.2 [4] An online survey of a large number of soccer fans determined that 65% follow European competitions and 55% follow local (South African) competitions while all of the fans follow at least one of the two activities. What proportion of soccer fans follow European competitions exclusively?

Find coefficient of correlation of the following data. Use this data to estimate y when x =

12.

X

3

6

7

10

Y

12

18

25

22

Suppose the mean expenditure per customer at a tire store is $80.00, with a standard deviation

of $10.00. If a random sample of 40 customers is taken, what is the probability

a) that the sample average expenditure per customer for this sample will be $87.00 or

less?

b) that the sample average expenditure per customer for this sample will be $87.00 or

more?

c) that the sample average expenditure per customer for this sample will be between

$70.00 and $85.00?

Find coefficient of correlation of the following data. Use this data to estimate y when x = 12

X 3 6 7 10

Y 12 18 25 22

The finished inside diameter of a piston ring is normally distributed with a mean of 10 centimeters and a standard deviation of 0.03 centimeter.

(a) What proportion of rings will have inside diameters exceeding 10.075 centimeters?

(b) What is the probability that a piston ring will have an inside diameter between 9.97 and 10:03 centimeters?

(c) Below what value of inside diameter will 15% of the piston rings fall?

A soft-drink machine is regulated so that it discharges an average of 200 milliliters per cup. If the amount of drink is normally distributed with a standard deviation equal to 15 milliliters,

(a) what fraction of the cups will contain more than 224 milliliters?

(b) what is the probability that a cup contains between 191 and 209 milliliters?

(c) how many cups will probably overflow if 230- milliliter cups are used for the next 1000 drinks?

(d) below what value do we get the smallest 25% of the drinks?

3. Given the normally distributed variable X with mean 18 and standard deviation 2.5, find

(a) P(X<15):

(h) P(17< X<21);

(c) the value of k such that P(X<k) = 0.2578;

(d) the value of k such that P(X> A) = 0.1539.

2. Given a normal distribution with = 200 and o² = 100, find

(a) the area below 214;

(b) the area above 179;

(c) the area between 188 and 206;

(d) the x value that has 80% of the area below it;

(e) the two x values containing the middle 75% of the area.

The Red Crescent Society Association reports that the average time it takes to respond to an emergency call is 25 minutes. Assume the variable is approximately normally distributed and the standard deviation is 4.5 minutes. Calculate the probability that the time it takes to respond to an emergency call in less than 15 minutes.