Ask question

Ask question

All categories

1 year ago

14

Crossett Trucking Company claims that the mean weight of its delivery trucks when they are fully loaded is 6,000 pounds and the

standard deviation is 150 pounds. Assume that the population follows the normal distribution. Forty trucks are randomly selected and weighed.Within what limits will 95% of the sample means occur?

1 answer:

solniwko [45]1 year ago

6 0

Answer:

(5953.52,6046.49)

Step-by-step explanation:

We are given the following in the question:

Mean, $\mu$ = 6,000 pounds

Sample size, n = 40

Alpha, α = 0.05

Standard deviation, σ = 150 pounds

95% Confidence interval:

$\mu \pm z_{critical}\frac{\sigma}{\sqrt{n}}$

Putting the values, we get,

$z_{critical}\text{ at}~\alpha_{0.05} = 1.96$

$6000 \pm 1.96(\dfrac{150}{\sqrt{40}} )\\\\ = 6000 \pm 46.4854=\\(5953.5146,6046.4854)\approx (5953.52,6046.49)$

are the limits within which 95% of the sample means occur.

You might be interested in

Your promotional budget for the year is $300 for personal selling, $300 for sales promotion, \$1,500 for advertising, and $500 f

aleksandr82 [10.1K]

Answer:

to get the total promotion budget for the year we will add $300 for personal selling plus $300 for sales promotion plus $1500 for advertising plus $500 for image promotion to the a total of 2600 dollars

8 0

2 years ago

It is claimed that 55% of marriages in the state of California end in divorce within the first 15 years. A large study was start

kykrilka [37]

Answer:

0.0045 = 0.45% probability that less than two of them ended in a divorce

Step-by-step explanation:

For each marriage, there are only two possible outcomes. Either it ended in divorce, or it did not. The probability of a marriage ending in divorce is independent of any other marriage. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

55% of marriages in the state of California end in divorce within the first 15 years.

This means that $p = 0.55$

Suppose 10 marriages are randomly selected.

This means that $n = 10$

What is the probability that less than two of them ended in a divorce?

This is

$P(X < 2) = P(X = 0) + P(X = 1)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{10,0}.(0.55)^{0}.(0.45)^{10} = 0.0003$

$P(X = 1) = C_{10,1}.(0.55)^{1}.(0.45)^{9} = 0.0042$

$P(X < 2) = P(X = 0) + P(X = 1) = 0.0003 + 0.0042 = 0.0045$

0.0045 = 0.45% probability that less than two of them ended in a divorce

8 0

1 year ago

A freight carrier charges $0.57 for a package weighing up to one ounce plus and additional $0.32 for each additional ounce or fr

kherson [118]

We have to write an equation that uses this info so we can find the cost to ship that package. However, the package weight is given to us in grams and we need it in ounces. So first thing we are going to do is convert that 224 g to ounces. Use the fact that 1 g = .035274 ounces to convert. $224g*\frac{.035274oz}{1g}$ . Do the multiplication and cancel out the label of grams and we have 7.901376 ounces. Ok. We know that it costs .57 to mail the package for the first ounce. We have almost 8 ounces. So no matter what, we are paying .57. For each additional ounce we are paying .32. The number of .32's we have to spend depends upon how much the package goes over the first ounce. For the first ounce we pay .57, then for the remaining 6.901376 ounces we pay .32 per ounce. Our equation looks like this: C(x) = .32(6.901376) + .57 and we need to solve for the cost, C(x). Doing the multiplication we find that it would cost $2.78 to ship that package.

3 0

2 years ago

If a(x) = 3x + 1 and b (x) = StartRoot x minus 4 EndRoot, what is the domain of (b circle a) (x)?

kiruha [24]

Answer:

$[1,\infty)$

Step-by-step explanation:

$b(x)=\sqrt{x-4}$

$a(x)=3x+1$

Since we want to know the domain of $(b \circ a)(x)$ , let's first consider the domain of the inside function, that is, that of $a(x)=3x+1$ . Every polynomial function has domain all real numbers.

So we can plug anything for function $a$ and get a number back.

Now the other function is going to be worrisome because it has a square root. You cannot take square root of negative numbers if you are only considering real numbers which that is the case with most texts.

Let's find $(b \circ a)(x)$ and simplify now.

$(b \circ a)(x)$

$b(a(x))$

$b(3x+1)$

$\sqrt{(3x+1)-4}$

$\sqrt{3x+1-4}$

$\sqrt{3x-3}$

Now again we can only square root positive or zero numbers so we want $3x-3 \ge 0$ .

Let's solve this to find the domain of $(b \circ a)(x)$ .

$3x-3 \ge 0$

Add 3 on both sides:

$3x \ge 3$

Divide both sides by 3:

$x \ge 1$

So we want $x$ to be a number greater than or equal to 1.

The option that says this is $[1,\infty)$

-------------------------------

Give an example why option A fails:

A number in the given set is -2.

$a(x)=3x+1$

$b(x)=\sqrt{x-4}$

So $a(-2)=3(-2)+1=-6+1=-5$ and $b(-5)=\sqrt{-5-4}=\sqrt{-9} \text{ which is not real}$ .

Give an example why option B fails:

A number in the given set is 0.

$a(x)=3x+1$

$b(x)=\sqrt{x-4}$

So $a(0)=3(0)+1=0+1=1$ and $b(1)=\sqrt{1-4}=\sqrt{-3} \text{ which is not real}$ .

Give an example why option D fails:

While all the numbers in set D work, there are more numbers outside that range of numbers that also work.

A number not in the given set that works is 3.

$a(x)=3x+1$

$b(x)=\sqrt{x-4}$

So $a(3)=3(3)+1=9+1=10$ and $b(1)=\sqrt{10-4}=\sqrt{6} \text{ which is real}$ .

4 0

2 years ago

Read 2 more answers

in one month, Jason earns $32.50 less than twice the amount Kevin earns Jason earns $212.50 write and solve an algebraic equatio

hoa [83]

So what I did was as $32.50 twice and got $65.00 and subtracted it with $212.50 and got $152.50. Hope i was helpful!

4 0

2 years ago

Read 2 more answers