What two consecutive numbers does 27 fall between
1 answer:
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Answer:
(a) The probability that the store’s revenues were at least $9,000 is 0.0233.
(b) The revenue of the store on the worst 1% of such days is $7,631.57.
Step-by-step explanation:
According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sum of values of X, i.e ∑X, will be approximately normally distributed.
Then, the mean of the distribution of the sum of values of X is given by,
And the standard deviation of the distribution of the sum of values of X is given by,
It is provided that:
As the sample size is quite large, i.e. <em>n</em> = 310 > 30, the central limit theorem can be applied to approximate the sampling distribution of the store’s revenues for Sundays by a normal distribution.
(a)
Compute the probability that the store’s revenues were at least $9,000 as follows:
Thus, the probability that the store’s revenues were at least $9,000 is 0.0233.
(b)
Let <em>s</em> denote the revenue of the store on the worst 1% of such days.
Then, P (S < s) = 0.01.
The corresponding <em>z-</em>value is, -2.33.
Compute the value of <em>s</em> as follows:
Thus, the revenue of the store on the worst 1% of such days is $7,631.57.
Both problems give you a function in the second column and the x-values. To find out the values of a through f, you need to plug in those x-values into the function and simplify!
You need to know three exponent rules to simplify these expressions:
1) The negative exponent rule says that when a base has a negative exponent, flip the base onto the other side of the fraction to make it into a positive exponent. For example,
.
2) Raising a fraction to a power is the same as separately raising the numerator and denominator to that power. For example,
.
3) The zero exponent rule<span> says that any number raised to zero is 1. For example,
.
</span>
Back to the Problem:
Problem 1
The x-values are in the left column. The title of the right column tells you that the function is
. The x-values are:
<span>1) x = 0
</span>Plug this into
to find letter a:
<span>
2) x = 2
</span>Plug this into to find letter b:
<span>
3) x = 4
</span>Plug this into to find letter c:
<span>
Problem 2
</span>The x-values are in the left column. The title of the right column tells you that the function is
. The x-values are:
<span>1) x = 0
</span>Plug this into
to find letter d:
<span>
2) x = 2
</span>Plug this into to find letter e:
<span>
3) x = 4
</span>Plug this into to find letter f:
<span>
-------
Answers:
a = 1
b = </span>
<span>
c = </span>
d = 1
e =
f =
You need to know three exponent rules to simplify these expressions:
1) The negative exponent rule says that when a base has a negative exponent, flip the base onto the other side of the fraction to make it into a positive exponent. For example,
2) Raising a fraction to a power is the same as separately raising the numerator and denominator to that power. For example,
3) The zero exponent rule<span> says that any number raised to zero is 1. For example,
</span>
Back to the Problem:
Problem 1
The x-values are in the left column. The title of the right column tells you that the function is
<span>1) x = 0
</span>Plug this into
<span>
2) x = 2
</span>Plug this into
<span>
3) x = 4
</span>Plug this into
<span>
Problem 2
</span>The x-values are in the left column. The title of the right column tells you that the function is
<span>1) x = 0
</span>Plug this into
<span>
2) x = 2
</span>Plug this into
<span>
3) x = 4
</span>Plug this into
<span>
-------
Answers:
a = 1
b = </span>
c = </span>
d = 1
e =
f =