648 divided by 18 using partial quotients

The average life of a bread-making machine is 7 years, with a standard deviation of 1 year. Assuming that the lives of these mac

Alina [70]

Answer:

a) $P(6.4$

b) $a=7 +1.036*0.333=7.345$

So the value of bread-making machine that separates the bottom 85% of data from the top 15% is 7.345.

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Let X the random variable life of a bread making machine. We know from the problem that the distribution for the random variable X is given by:

$X\sim N(\mu =7,\sigma =1)$

We take a sample of n=9 . That represent the sample size.

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is also normal and is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

$\bar X \sim N(\mu=7, \frac{1}{\sqrt{9}})$

Solution to the problem

Part a

(a) the probability that the mean life of a random sample of 9 such machines falls between 6.4 and 7.2

In order to answer this question we can use the z score in order to find the probabilities, the formula given by:

$z=\frac{\bar X- \mu}{\frac{\sigma}{\sqrt{n}}}$

The standard error is given by this formula:

$Se=\frac{\sigma}{\sqrt{n}}=\frac{1}{\sqrt{9}}=0.333$

We want this probability:

$P(6.4$

Part b

b) The value of x to the right of which 15% of the means computed from random samples of size 9 would fall.

For this part we want to find a value a, such that we satisfy this condition:

$P(\bar X>a)=0.15$ (a)

$P(\bar X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.85 of the area on the left and 0.15 of the area on the right it's z=1.036. On this case P(Z<1.036)=0.85 and P(Z>1.036)=0.15

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=1.036$

And if we solve for a we got

$a=7 +1.036*0.333=7.345$

So the value of bread-making machine that separates the bottom 85% of data from the top 15% is 7.345.

8 0

4 years ago

The length of a rectangle is 4 times its width. The perimeter of the rectangle is 50 cm long. What is the area of the rectangle?

Eduardwww [97]

The answer would be 100

3 0

3 years ago

a petting zoo has 5 lambs 11 rabbits 4 goats and 4 piglets. find the ratio of goats to the total number of animals. write the ra

kolbaska11 [484]

Answer:

1:6 or 1/6

Step-by-step explanation:

Because the question asks for the goats to the total number of animals, you have to write the ratio in the same order. So, there are 4 goats, and to find the total number of animals, you just add every number.

5+11+4+4=24

The result would be 4:24, and because you need the ratio in the simplest form, you just divide both sides by the same greatest number. Both 4 and 24 can be divided evenly by 4. So, when you simplify, the answer comes out as 1:6. (Ratios can also be written as fractions, just so you know!! For example, the ratio 1:6 can be written as 1/6; both answers would be correct.)

Hope this helps!!!! Have an amazing day :3

7 0

4 years ago

Mr. and Mrs. Brown went to two movies. The first one lasted 3 1/2 hours and the second one lasted 1 1/3 hours . How much longer

STALIN [3.7K]

Answer:

2 1/6 longer

Step-by-step explanation:

3 1/2-1 1/3

7/2 - 4/3

21/6-8/6

13/6 or 2 1/6

so 2 1/6 longer.

Hope this helps :D

6 0

3 years ago

Read 2 more answers

760 hundreds<br> Rename the number. use the place-value chart to help

Damm [24]

<span>760 hundreds, we need to rename this given value.
First we need to analyze the given digits
=> 760 hundreds = 760 000
=> hundreds has 3 digits, starting from ones, tens and hundreds. Thus, we need to add hundreds value to 760
=> that make 760 hundreds or 700 000 + 60 000
=> 760 000 (7 is hundred thousands, 6 is ten thousands)
That’s how you are going to rename a given value, you must first determine each value of the given digits</span>

6 0

3 years ago