The Historical average is 35 minutes with a population standard deviation of 8 minutes. A test of the new process on 10 random runs has a mean of 33 minutes. They are only testing for a reduction in the mean. What is the critical value for an Alpha level of 5%. Assume normality.

We need to conduct a hypothesis in order to check if the mean is lower than 35 min, the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

For the critical value since we are conducting a left tailed test we neeed to find on the normal satandard distribution a quantile who accumulates 0.05 of the area in the left and we got:

And if the statistic calculated is lower than the critical value we relect the null hypothesis otherwise we FAIL to reject the null hypothesis at the significance level given.

Step-by-step explanation:

Data given and notation  

represent the sample mean

represent the population standard deviation

sample size  

represent the value that we want to test

represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is lower than 35 min, the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

For the critical value since we are conducting a left tailed test we neeed to find on the normal satandard distribution a quantile who accumulates 0.05 of the area in the left and we got:

And if the statistic calculated is lower than the critical value we relect the null hypothesis otherwise we FAIL to reject the null hypothesis at the significance level given.

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47

an

y = 6x -3y -12

y +3y +12 = 6x

=> . x = { 2y / 3 +2 } this is equation of line in terms of x

=> . if line meets the x-axis the co-ordinates of meeting point would be ( x , 0 )

=> . x = 2 ( 0 ) / 3 + 2

=> . x = 2

so, the point is ( 2 , 0 )