Answer:
The probability that the sample proportion is within 0.03 of the population proportion is 0.468.
Step-by-step explanation:
The complete question is:
A company makes auto batteries. They claim that 84% of their LL70 batteries are good for 70 months or longer. Assume that this claim is true. Let p^ be the proportion in a random sample of 60 such batteries that are good for 70 months or more. What is the probability that this sample proportion is within 0.03 of the population proportion? Round your answer to two decimal places.
Solution:
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
The standard deviation of this sampling distribution of sample proportion is:
The information provided is:
As the sample size is large, i.e. <em>n</em> = 60 > 30, the Central limit theorem can be used to approximate the sampling distribution of sample proportion of LL70 batteries that are good for 70 months or longer.
Compute the probability that the sample proportion is within 0.03 of the population proportion as follows:
Thus, the probability that the sample proportion is within 0.03 of the population proportion is 0.468.
First, change 7 2/3 to an improper fraction
7 x 3 = 21 + 2 = 23
23/3 is the amount Maria made
Find a common denominator for all: 24
(23/3)(8/8) = 184/24
(5/6)(4/4) = 20/24
Subtract the amount she drank from the whole
184/24 - 20/24 = 164/24
Find 3/4 of the bottle
(164/24)(3/4) = 5.125
finally, divide the number gotten with 3
5.125/3 = 1.70
1.70 pints were in each bottle.
hope this helps
All estimating problems make the assumption you are familar with your math facts, addition and multiplication. Since students normally memorize multiplication facts for single-digit numbers, any problem that can be simplified to single-digit numbers is easily worked.
2. You are asked to estimate 47.99 times 0.6. The problem statement suggests you do this by multiplying 50 times 0.6. That product is the same as 5 × 6, which is a math fact you have memorized. You know this because
.. 50 × 0.6 = (5 × 10) × (6 × 1/10)
.. = (5 × 6) × (10 ×1/10) . . . . . . . . . . . by the associative property of multiplication
.. = 30 × 1
.. = 30
3. You have not provided any clue as to the procedure reviewed in the lesson. Using a calculator,
.. 47.99 × 0.6 = 28.79 . . . . . . rounded to cents
4. You have to decide if knowing the price is near $30 is sufficient information, or whether you need to know it is precisely $28.79. In my opinion, knowing it is near $30 is good enough, unless I'm having to count pennies for any of several possible reasons.
Answer:
Step-by-step explanation:
Hello!
The variable of interest is the weight in ounces of a soap bar.
Attached is a QQplot diagram.
A Q-Q plot is a diagram that compares two probability distributions, in this case, the probability distribution of the data set against the theoretical normal distribution. If the observed data matches the theoretical sets, you can say that that population follows said distribution.
As you can see in the graphic the observed values (blue dots) fit the normal theoretical quantiles, so we can say that the data appear to come from a normal distribution.
I hope it helps.
Answer:
The scale factor for the resultant rectangle is
units.
Step-by-step explanation:
Given two rectangles with sides 3 units and 7.5 units.
We have to find the scaling factors so that we can obtain bigger rectangle of 7.5 units from smaller rectangle of 3 units.
Scale factor is defined as the ratio of corresponding side of given figure to the corresponding side of resulting figure.
That is 
Here, 
Hence, the scale factor for the resultant rectangle is units.
