Answer:
m < -6
Step-by-step explanation:
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Answer: 1%
Explanation:
Add up the frequencies in the bottom row: 350+200+245+125+66+10+4 = 1000
There are 1000 families total. Of this total, 10+4 = 14 families have more than six people. I added up the frequency counts for "7 people" and "8 people" to get 14.
Divide 14 over 1000 and we get 14/1000 = 0.014 = 1.4% which rounds to 1%
Answer: a. CI for the mean: 17.327 < μ < 26.473
b. CI for variance: 29.7532 ≤
≤ 170.9093
Step-by-step explanation:
a. To construct a 95% confidence interval for the mean:
The given data are:
mean = 21.9
s = 7.7
n = 12
df = 12 - 1 = 11
1 - α = 0.05
= 0.025
t-score =
= 2.2001
Note: since the sample population is less than 30, it is used a t-score.
The formula for interval:
mean ± 
Substituing values:
21.9 ± 2.200.
21.9 ± 4.573
The interval is: 17.327 < μ < 26.473
b. A 95% confidence interval for the variance:
The given values are:
= 
= 59.29
α = 0.05
= 0.025
= 0.975
= 21.92
= 3.816
Note: To find the values for
and
, look for them at the chi-square table
The formula to calculate interval:
(
)
are the lower and upper limits, respectively.
Substituing values:
(
)
(29.7532, 170.9093)
The interval for variance is: 29.7532 ≤
≤ 170.9093
Use cosine law to solve the problem. See image attached.
What we're looking for is the length of side A (a side which is opposite with angle A).
This is the formula of cosine law
A² = B² + C² - 2BC cos A
Input the numbers
A² = 75² + 90² - 2(75)(90) cos 85°
A =

A =