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:
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:
.
The answer is 42 why, because 42 divided by 6 equals 7 plus 14 is 21 and then you double it so it's 42.
First you would need to add up all of the data given, then divide the sum by 9 because there is 9 pieces of data. So it would be 229/9=25.4444444 repeating.
Answer:
Halle bought 6 plums from the store.
Step-by-step explanation:
Given:
total cost of the peaches = $1.88
Cost of 1 Plum = $0.33
Total Money paid = $3.86
We need to find the number of Plums.
Let the number of plums be x.
Now we know that Total money paid is equal to Cost of peaches plus Cost of each Plum multiplied with number of plums.
Hence the expression can be framed as;

Now Solving the above expression to find the value of x;

Hence Halle bought 6 plums from the store.
Answer:
B. 
Step-by-step explanation:
Let
, we proceed to find its equivalent expression by applying logarithm properties:
1)
Given.
2)
Definition of logarithm.
3)

4)

5)
Compatibility with addition/Existence of additive inverse/Modulative property
6)
Symmetrical property/Result.
Hence, the right answer is B.