manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 433.0 gram setting. It is believed that the machine is underfilling the bags. A 40 bag sample had a mean of 431.0 grams. A level of significance of 0.1 will be used. Is there sufficient evidence to support the claim that the bags are underfilled

Since the calculated value of Z= -0.01871 does not lie in the critical region

Z ≥ Z∝ =± 1.28 we conclude that the null hypothesis is true and there is not sufficient evidence to support the claim that the bags are under filled.

Step-by-step explanation:

We formulate hypotheses as

H0: u < 433.0   against  the claim  Ha: u ≥ 433.0  ( one sided)

The significance level ∝= 0.1

Since the sample size n= 40 is greater then 30 z test is used.

Z = X`- u/ S/ √n

Z= 431.0- 433/ 676/√40

z= -2/106.8859

Z= -0.01871

The critical region is Z ≥ Z∝ =± 1.28 for one tailed test at alpha= 0.1

Since the calculated value of Z does not lie in the critical region we conclude that the null hypothesis is true and there is not sufficient evidence to support that the bags are under filled.

.24

step-by-step explanation:

the probability is   .24

the first player had the highest probability of getting a silver marble

the game could be made fair by adding back the marble that was drawn after each draw

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is