Mathematics, 06.04.2020 16:27 shjblover812

Amy works for a company that produces plastic lids and cups for restaurants. She wants to estimate what proportion of lids produced in a day have a defect that makes them not fit the cups. She takes a random sample of 250 250250 lids from the more than 10 , 000 total lids produced that day and finds 15 lids in the sample with this defect. Based on this sample, calculate the 99% confidence interval for the proportion of lids produced that day with this defect?

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99% confidence interval for the proportion of lids produced that day with this defect somewhere between ( .0213 , .0987) or between $2.13\%$ to $9.87\%$

Step-by-step explanation:

Given -

Sample size ( n) = 250

Sample proportion $(\widehat{p})$ = $\frac{15}{250}$ = .06

$\alpha = 1 -$ confidence interval = 1 - .99 = .01

$z_{\frac{\alpha}{2}}$ = $z_{\frac{.01}{2}}$ = 2.58

99% confidence interval for the proportion of lids produced that day with this defect = $\widehat{p} \pm z_{\frac{\alpha}{2}} \sqrt{\frac{(\widehat{p}) (1 - \widehat{p}) }{n}}$

= $.06 \pm z_{\frac{.01}{2}} \sqrt{\frac{(.06) (1 - .06) }{250}}$

= $.06 \pm 2.58\times .0150$

= $.06 \pm .0387$

= ( .06 + .0387 ) , ( .06 - .0387 )

= ( .0987 , .0213 )

Answer from: heyyyyy117

(0.021,0.099)

Step-by-step explanation:

khan

Answer from: Quest

Igotchu on that if you still need it

Answer from: Quest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.