Compute 95% confidence intervals for the proportion of defective items in a process when it is found that a sample of size 100 yields 8 defectives.

0.02683<x<0.133173

Step-by-step explanation:

The confidence interval formula is expressed as;

CI = p ± z√p(1-p)/n

p is the proportion

z is the confidence interval at 95% confidence

n is the sample size

Since it is found that a sample of size 100 yields 8 defectives, the sample proportion p = 8/100 = 0.08

Given

n = 100

z score = 1.96

p = 0.08

1-p = 1-0.08 = 0.92

Required

95% confidence interval

Substitute the given parameters into the formula as shown;

CI = p ± z√p(1-p)/n

CI = 0.08 ± 1.96√0.08(0.92)/100

CI = 0.08 ± 1.96√0.0736/100

CI = 0.08 ± 1.96(0.027129)

CI = 0.08 ± 0.053173

CI = (0.08-0.053173, 0.08+0.053173)

CI = (0.02683, 0.133173)

Hence the 95% confidence intervals for the proportion of defective items is 0.02683<x<0.133173

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."