Round 12,351 to the nearest hundred

The operation manager at a tire manufacturing company believes that the mean mileage of a tire is 30,393 miles, with a standard

Pie

Answer:

52.84% probability that the sample mean would differ from the population mean by less than 339 miles in a sample of 37 tires if the manager is correct

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem:

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 30393, \sigma = 2876, n = 37, s = \frac{2876}{\sqrt{37}} = 472.81$

What is the probability that the sample mean would differ from the population mean by less than 339 miles in a sample of 37 tires if the manager is correct

This probability is the pvalue of Z when X = 30393 + 339 = 30732 subtracted by the pvalue of Z when X = 30393 - 339 = 30054. So

X = 30732

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{30732 - 30393}{472.81}$

$Z = 0.72$

$Z = 0.72$ has a pvalue of 0.7642.

X = 30054

$Z = \frac{X - \mu}{s}$

$Z = \frac{30054 - 30393}{472.81}$

$Z = -0.72$

$Z = -0.72$ has a pvalue of 0.2358

0.7642 - 0.2358 = 0.5284

52.84% probability that the sample mean would differ from the population mean by less than 339 miles in a sample of 37 tires if the manager is correct

4 0

3 years ago

What is the value of the discriminant, b2 − 4ac, for the quadratic equation 0 = x2 − 4x + 5, and what does it mean about the num

Aleksandr-060686 [28]

So discriminant gives us 3 possibilites connected with result of the equation b^2-4ac. If it is bigger than zero, there are 2 solutions, if answer is exactly 0, then there is one answer and if the number is lower than 0, there are no solutions.

Discriminant of your quadratic equation is (-4)^2-4*1*5=16-20=-4, so there are no solutions.

3 0

3 years ago

Read 2 more answers

A dog walker charges a flat rate of $6 per walk plus an hourly rate of $30. How much does the dog walkercharge for a 45 minute w

leonid [27]

hello

from the question given, the dog walker charges a flat rate of $6 and an extra $30 per hour.

we can write out an equation in function notation

let the number of hours be represented by x

$f(x)=6+30x$

now we can proceed to solve the cost of the walk for 45 minutes

$\begin{gathered} 1hr=60\min s \\ \text{xhr}=45\min s \\ x=\frac{45}{60} \\ x=\frac{3}{4} \\ \text{therefore 45mins = 3/4 hours} \end{gathered}$

now we can input the value into the equation and know the cost for 45 minutes walk

$\begin{gathered} f(x)=6+30x \\ x=\frac{3}{4} \\ f(x)=6+30(\frac{3}{4}) \\ f(x)=6+22.5 \\ f(x)=28.5 \end{gathered}$

from the calculation above, the cost of 45 minutes walk will cost $28.5

6 0

1 year ago

What is the value of y?

alexira [117]

9514 1404 393

Answer:

y = 8√3

Step-by-step explanation:

In the 30°-60°-90° "special" triangle, the ratio of sides lengths is ...

1 : √3 : 2 = 8 : y : hypotenuse

In order for these ratios to be equal, we must have ...

y = 8√3

__

If you want to solve this using your trig skills, you recognize that ...

Tan = Opposite/Adjacent

tan(30°) = 8/y

y = 8/tan(30°) . . . . where tan(30°) = 1/√3

y = 8√3

4 0

2 years ago

Last winter, Tom earned $47.50 shoveling snow and $122 giving ice-skating lessons. During the summer, he earned twice as much by

siniylev [52]

You would have to add 47.50 + 122 to get 169.5 dollars. to get the amount of money he made in the summer, you would have to multiply 169.5 by 2 which would equal 339 dollars. so he made 339 dollars over the summer :)

5 0

3 years ago