Mathematics, 25.03.2020 02:08 alicat20

A police officer would like to estimate the proportion of petty theft cases that have gone unsolved in a large city. He takes a random sample of 81 petty theft cases and finds 52 of these have gone unsolved. Set up the equation for the 95% confidence interval for p.

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Answer from: jessebeck0805

95% confidence interval for p is [0.54 , 0.75].

Step-by-step explanation:

We are given that a police officer would like to estimate the proportion of petty theft cases that have gone unsolved in a large city. He takes a random sample of 81 petty theft cases and finds 52 of these have gone unsolved.

Let p = population proportion of petty theft cases

So, the pivotal quantity for 95% confidence interval for population proportion p is given by;

P.Q. = $\frac{\hat p -p}{\sqrt{\frac{\hat p(1- \hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = proportion of petty theft cases that have gone unsolved in a large city in a sample of 81 cases = $\frac{52}{81}$

n = sample of cases = 81

So, 95% confidence interval for the population proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95

P(-1.96 < $\frac{\hat p -p}{\sqrt{\frac{\hat p(1- \hat p)}{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\sqrt{\frac{\hat p(1- \hat p)}{n} } }$ < ${\hat p -p}$ < $1.96 \times {\sqrt{\frac{\hat p(1- \hat p)}{n} } }$ ) = 0.95

P( $\hat p -1.96 \times {\sqrt{\frac{\hat p(1- \hat p)}{n} } }$ < p < $\hat p +1.96 \times {\sqrt{\frac{\hat p(1- \hat p)}{n} } }$ ) = 0.95

95% confidence interval for p = [ $\hat p -1.96 \times {\sqrt{\frac{\hat p(1- \hat p)}{n} } }$ , $\hat p +1.96 \times {\sqrt{\frac{\hat p(1- \hat p)}{n} } }$ ]

= [ $\frac{52}{81} -1.96 \times {\sqrt{\frac{\frac{52}{81} (1- \frac{52}{81} )}{81} } }$ , $\frac{52}{81} +1.96 \times {\sqrt{\frac{\frac{52}{81} (1- \frac{52}{81} )}{81} } }$ ]

= [0.54 , 0.75]

Therefore, 95% confidence interval for p is [0.54 , 0.75].

Answer from: Quest

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841

Lots of points! show all of your work! i need #9-#14 and 12 + 16!

Answer from: Quest

a) 7x=7

step-by-step explanation:

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