Iwant to know which of two manufacturing methods will be better. i create 10 prototypes using the first process and 10 using the second. there were three defectives in the first batch and five in the second. what is a 95% confidence interval for the difference in the proportion of defectives?

(-0.620, 0.220)

Step-by-step explanation:

The formula to find the confidence interval for the difference in true proportion of the two groups. is given by :-

, where = Sample size for first group.

= Sample size for second group.

= Sample proportion for first group.

= Sample proportion for second group.

z* = critical z-value.

Let first group be "group of prototypes by first process " and second group be "group of prototypes by second process".

= Proportion of defectives in the first batch.

= Proportion of defectives in the second batch.

From question , we have

,  ,  ,

By z-table , Critical value for 95% confidence interval is z* =1.96.

Substitute all values in formula , we get

Hence,  a 95% confidence interval for the difference in the proportion of defectives is (-0.620, 0.220).

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step-by-step explanation:

11.2

step-by-step explanation:

when doing tangent the tangent of the angle is equal to the opposite side from the angle over the adjacent side to the angle.

tan43 = x / 12

move 12 over by multiplying each side by 12

12tan43 = x

x = about 11.2