The production manager for the xyz manufacturing company is concerned that the customer orders are being shipped late. he asked one of his planners to check the timeliness of shipments for 900 orders. the planner randomly selected 900 orders and found that 180 orders were shipped late. construct the 95% confidence interval for the proportion of orders shipped late.

The 95% confidence interval would be given (0.174;0.226).

We are confident (95%) that true proportion of orders that were shipped late is between 0.174 and 0.226

Step-by-step explanation:

Data given and notation  

n=900 represent the random sample taken    

X=180 represent the orders that were shipped late

estimated proportion of the orders that were shipped late

represent the significance level (no given, but is assumed)    

p= population proportion of orders that were shipped late

The confidence interval would be given by this formula

For the 95% confidence interval the value of and , with that value we can find the quantile required for the interval in the normal standard distribution.

And replacing into the confidence interval formula we got:

And the 95% confidence interval would be given (0.174;0.226).

We are confident (95%) that true proportion of orders that were shipped late is between 0.174 and 0.226

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

hi how are you doing today, if you need just ask me.

step-by-step explanation: