1Suppose the average consumption of water per person per yea

1.Suppose the average consumption of water per person per year is 23.4 gallons with a standard deviation of 7.1 gallons. Suppose you conducted a sample of 40 individuals, what is the probability that their annual average water consumption is less than 25 gallons?

2. Suppose an average weight of boxer is 245.7 pounds with a standard deviation of 34.5 pounds, but the probability distribution is Unknown. Suppose you conducted a random sample of 32 boxers, what is the probability that the average weight of the sample will be less than 234 pounds?

3. Assume that the systolic blood pressure of a 30 year old person is normally distributed, with an average of 122 Millimeters of Mercury (mmHg) and a standard deviation of 10 mmHg. Suppose you conducted a sample of 16 individuals from the 30 year old group. calculate the probability that the average blood pressure of the sample will be greater than 125 mmHg.

4. If the first three numbers are selected to estimate the average number of all 10 number, what is the sampling error?

36,29,55,22,34,67,30,41,35,21

Solution

mu- average consumption of water per person = 23.4

sigma = 7.1

n = sample size =40

x bar mean of sample is normal (mu, sigma/rtn)

= (23.4,1.123)

X bar < 25 implies

Z score <1.6/1.123

or z<1.425

Prob = 0.9236

----------------------------------------------------

2) mu = 245.7

sigma 34.5

Even if the prob distribution is not know when n>30, means follow a normal distribution.

with mean = 245.7 and std error = 34.5/rt 32

= 6.099

Hence Prob (x bar<234(

= P(Z<-11.7/6.099)

=P(Z<-1.92)

= 0.0274

-------------------------------------

3) X - systolic pressure of a 30 year old man

N(122, 10)

Sample size =16

std error of sample = 10/4 = 2.5

P(X.>125) =P(Z>3/2.5) = P(Z>1.17)

=0.1210

-------------------------------------------------

4) Real average= 0370/10 =37

If average is calculated from first three numbers alone average = 120/3 =40

Hence sampling error = +3