The question has a period I don’t know why
1 answer:
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Answer:
The population standard deviation is not known.
90% Confidence interval by T₁₀-distribution: (38.3, 53.7).
Step-by-step explanation:
The "standard deviation" of $14 comes from a survey. In other words, the true population standard deviation is not known, and the $14 here is an estimate. Thus, find the confidence interval with the Student t-distribution. The sample size is 11. The degree of freedom is thus .
Start by finding 1/2 the width of this confidence interval. The confidence level of this interval is 90%. In other words, the area under the bell curve within this interval is 0.90. However, this curve is symmetric. As a result,
- The area to the left of the lower end of the interval shall be
.
- The area to the left of the upper end of the interval shall be
.
Look up the t-score of the upper end on an inverse t-table. Focus on the entry with
- a degree of freedom of 10, and
- a cumulative probability of 0.95.
.
This value can also be found with technology.
The formula for 1/2 the width of a confidence interval where standard deviation is unknown (only an estimate) is:
,
where
is the t-score at the upper end of the interval,
is the unbiased estimate for the standard deviation, and
is the sample size.
For this confidence interval:
,
, and
.
Hence the width of the 90% confidence interval is
.
The confidence interval is centered at the unbiased estimate of the population mean. The 90% confidence interval will be approximately:
.
Answer:
c = 11.03 m
Step-by-step explanation:
In this given <em>right isoceles triangle</em>, one of the sides are labeled as 7.8 m. We'll label this side as "a."
The length of side "a" is congruent to the other side. Therefore, the measurement of the other side is also 7.8 m.
We can use the Pythagorean Theorem to solve for the measurement of the hypotenuse, side "c."
According to the Pythagorean Theorem: .
We'll plug in the values for side "a" and side "b" into the formula:
To calculate the value of "c," we must take the squared root of :
c = 11.03087 m or 11.03 m
By the way, the value of c = <em>a </em>