We have the survey data on the body mass index ( BMI) of 664 young women. The mean BMI in the sample was . We treated these data as an SRS from a Normally distributed population with standard deviation 7.4. Give confidence intervals for the mean BMI and the margins of error for 90%, 95%, and 99% confidence. Interval (0.01)? margins of error (0.0001)?

Step-by-step explanation:

Margin of error = critical value × standard error

The standard error is:

s = σ / √n

s = 7.4 / √664

s = 0.287

The population is normally distributed, so the critical value can be found from a z-score table.

For 90% confidence, z = 1.645.

For 95% confidence, z = 1.960.

For 99% confidence, z = 2.576.

The margins of error are:

90%: 1.645 × 0.287 = 0.4724

95%: 1.960 × 0.287 = 0.5629

99%: 2.576 × 0.287 = 0.7398

The mean is 26.6, so the confidence intervals are:

90%: (26.6 − 0.47, 26.6 + 0.47) = (26.13, 27.07)

95%: (26.6 − 0.56, 26.6 + 0.56) = (26.04, 27.16)

99%: (26.6 − 0.74, 26.6 + 0.74) = (25.86, 27.34)

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

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