The aluminum association reports that the average american uses 56.8 pounds of aluminum in a year. a random sample of 50 households is monitored for one year to determine aluminum usage. if the population standard deviation of annual usage is 12.1 pounds, what is the probability that the sample mean will be each of the following? appendix a statistical tablesa. more than 58 poundsb. more than 57 poundsc. between 55 and 57 poundsd. less than 53 poundse. less than 48 pounds

A)what is the probability that the sample mean will be More than 58 pounds

P(x>58)

Formula :

Substitute the values :

refer the z table

P(x<58)=0.5359

P(X>58)=1-P(x<58)=1-0.5359=0.4641

Hence the probability that the sample mean will be More than 58 pounds is 0.4641

B)what is the probability that the sample mean will be More than 57 pounds

P(x>57)

Formula :

Substitute the values :

refer the z table

P(x<57)=0.5040

P(X>57)=1-P(x<57)=1-0.5040=0.496

Hence the probability that the sample mean will be More than 57 pounds is 0.496

C)what is the probability that the sample mean will be Between 55 and 57 pound

Formula :

Substitute the values :

refer the z table

P(x<57)=0.5040

Formula :

Substitute the values :

refer the z table

P(x<55)=0.4443

P(55<x<57)=P9x<57)-P(x<55) =0.5040-0.4443=0.0597

Hence the probability that the sample mean will be Between 55 and 57 pounds is 0.0597

D)what is the probability that the sample mean will be Less than 53 pounds

Formula :

Substitute the values :

refer the z table

P(x<53)=0.3783

The probability that the sample mean will be Less than 53 pounds is 0.3783

E)what is the probability that the sample mean will be Less than 48 pounds

Formula :

Substitute the values :

refer the z table

P(x<48)=0.2358

The probability that the sample mean will be Less than 48 pounds is 0.2358

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

i found the koficent of the linear function and i foun c acordind to the strict formula y=kx+c and then i took 2 as an x and replacet it on the formula i found and then foun the y