What is the value of the expression below when x 5 and y = 5? 6x

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

A right angled triangle has sides of length 9cm, 12cm and 15cm. Calculate its area in square centimetres.

Dmitriy789 [7]

The area of a right angled triangle with sides of length 9cm, 12cm and 15cm in square centimeters is 54 sq cm.

The formula to calculate the area of a right triangle is given by:

Area of Right Triangle, A = (½) × b × h square units

Where, “b” is the base (adjacent side) and “h” is the height (perpendicular side). Hence, the area of the right triangle is the product of base and height and then divide the product by 2.

We know that the hypotenuse is the longest side. So, the area of a right angled triangle will be half of the product of the remaining two sides.

Given sides of the triangle:

a=9cm

b=12cm

c=15cm

From this we know that the hypotenuse is c. Are of the triangle will be obtained by the other two sides.

∴Area = $\frac{1}{2}$ x 9 x 12

= 54 $cm^{2}$

5 0

1 year ago

What number is the highest 0.542 or 0.524

Vera_Pavlovna [14]

Answer:

0. 542

Step-by-step explanation:

8 0

3 years ago

Tarun has 4 more than the twice the number of tshirts Deepak has.Mahesh has 2 more than thrice the number of T-shirts that Tarun

Dafna11 [192]

Answer:

Deepak: 4 t-shirts,

Tarun: 12 t-shirts,

Mahesh: 14 t-shirts.

Step-by-step explanation:

Let x represent number of t-shirts that Deepak has.

Please consider the complete question.

Tarun has 4 t-shirt more than twice the number of T-shirts Deepak has. Mahesh has 2 more than thrice the number of T-shirts Deepak has. If the ratio of the t-shirt that Tarun and Mahesh have is 6 : 7, find out the number of the t-shirt each of them has.

Since Tarun has 4 t-shirt more than twice the number of T-shirts Deepak has, so the number of t-shirts that Tarun has would be $2x+4$ .

We are also told that Mahesh has 2 more than thrice the number of T-shirts Deepak has. So the number of t-shirts that Mahesh has would be $3x+2$ .

Since the ratio of the t-shirt that Tarun and Mahesh have is 6 : 7, so we can represent this information in an equation as:

$\frac{2x+4}{3x+2}=\frac{6}{7}$

Cross multiply:

$6(3x+2)=7(2x+4)$

$18x+12=14x+28$

$18x-14x+12-12=14x-14x+28-12$

$4x=16$

$x=\frac{16}{4}=4$

Therefore, Deepak has 4 t-shirts.

The number of t-shirts that Tarun has would be $2x+4\Rightarrow 2(4)+4=4+4=12$

Therefore, Tarun has 12 t-shirts.

The number of t-shirts that Mahesh has would be $3x+2\Rightarrow 3(4)+2=12+2=14$

Therefore, Mahesh has 14 t-shirts.

5 0

3 years ago

A recent survey found that 80% of jeans have back pockets, 65% have front pockets, and 48% have both back and

OlgaM077 [116]

Answer:

.52

Step-by-step explanation:

its only a little bit over a 50% chance to get a front pocketed jean, then to also have back pockets is under 50% chance so when you even those it comes to .52

5 0

3 years ago

What is the value of the expression below when x 5 and y = 5? 6x — бу – -​

What is the value of the expression below when x 5 and y = 5? 6x — бу – -