MATHEMATICS COLLEGE

The tread life of tires mounted on light-duty trucks follows the normal probability distribution with a mean of 60,000 miles and a standard deviation of 4,000 miles. Suppose you bought a set of four tires, what is the likelihood the mean tire life of these four tires is between 57,000 and 63,000 miles

Answers

Answer 1

Answer:

Answer:

86.64% probability that the mean tire life of these four tires is between 57,000 and 63,000 miles

Step-by-step explanation:

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

Normal probability distribution:

Problems of normally distributed samples can be 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:

$Z = (X - \mu)/(\sigma)$

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 $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = (\sigma)/(√(n))$

In this problem, we have that:

$\mu = 60000, \sigma = 4000, n = 4, s = (4000)/(√(4)) = 2000$

Suppose you bought a set of four tires, what is the likelihood the mean tire life of these four tires is between 57,000 and 63,000 miles

This is the pvalue of Z when X = 63000 subtracted by the pvalue of Z when X = 57000. So

X = 63000

$Z = (X - \mu)/(\sigma)$

By the Central Limit Theorem

$Z = (X - \mu)/(s)$

$Z = (63000 - 60000)/(2000)$

$Z = 1.5$

$Z = 1.5$ has a pvalue of 0.9332

X = 57000

$Z = (X - \mu)/(s)$

$Z = (57000 - 60000)/(2000)$

$Z = -1.5$

$Z = -1.5$ has a pvalue of 0.0668

0.9332 - 0.0668 = 0.8664

86.64% probability that the mean tire life of these four tires is between 57,000 and 63,000 miles

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NEEd help quickly please!!! The basketball game had 500 people in attendance. If the ratio of Pioneer fans to Lion fans is 15:5, how many MORE Pioneer fans were there? Pls use tape diagram.

Answers

Answer:

Step-by-step explanation:

15(500/20)-5(500/20)

375-125

250

There were 250 more Pioneer fans than Lion fans.

Please help me with this

Answers

Answer:x^2+10x+24

Step-by-step explanation:

Area of rectangle=length x width

Area of rectangle=(x+4)(x+6)

Area of rectangle=x^2+6x+4x+24

Area of rectangle=x^2+10x+24

28.2% of 92 this is for math

Answers

Hey there!

Usually when you come across the word “of” in mathematical problems , it simply means that you’re multiplying

So we can simply multiply 28.2% from 92

28.2% = 28.2/100 = 0.282

New equation

0.282 * 92 = the answer

0.282 * 92 = 25.944

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

What is the answer hurry please
36k = -9

Answers

Answer:

k=-0.25

Step-by-step explanation:

Convert 32/5 to a mixed number.

Answers

The mixed form of the factor 32/5 will be 6²/₅.

To convert the fraction 32/5 to a mixed number, we need to find the whole number part and the fractional part.

Divide the numerator (32) by the denominator (5) to find the whole number part. In this case, 32 divided by 5 equals 6 with a remainder of 2.

The quotient, 6, represents the whole number part of the mixed number.

The remainder, 2, represents the numerator of the fractional part.

The denominator remains the same.

Putting it all together, the mixed number representation of 32/5 is 6 and 2/5.

So, 32/5 is equal to 6 and 2/5.

To know more about mixed numbers follow

brainly.com/question/18120044

#SPJ6

Answer:

6 2/5

Step-by-step explanation:

6×5= 30 + 2= 32

I hope this helps in any way.

In the diagram shown, M, N and P are collinear and QM=QN as shown. If mMQN = 48" andmNQP = 33. Justify why QNP must be isosceles.

Answers

An isosceles triangle is that the triangle must have two sides of equal length.

Triangle QNP is isosceles triangle because, QN = PN

In triangle QMN,

Since, QM = QN

So, ∠QMN = ∠QNM

By property of triangle:

∠MQN + ∠QNM + ∠QMN = 180

48 + 2 ∠QNM = 180

∠QNM = $(180-48)/(2)$ = 66 degree

So, ∠QMN = ∠QNM = 66 degree

from figure,

∠QNM + ∠QNP = 180

∠QNP = 180 - 66 = 114 degree.

In triangle QNP,

∠QNP + ∠PQN + ∠QPN = 180

∠QPN = 180 - 33 - 114 = 33 degree

Since, ∠QNP = ∠QPN = 33 degree

Therefore, triangle QNP is isosceles triangle.

Learn more:

brainly.com/question/19414224

Answer/Step-by-step explanation:

Let's find the measure of the angles of ∆QNP.

∆QMN is am isosceles ∆, because it has two equal sides. Therefore, its base angles would be the same. Thus:

m<MNQ = ½(180 - 48) (one of the base angles of ∆QMN)

m<MNQ = ½(132) = 66°

Next, find m<QNP

m<QNP = 180° - m<MNQ (linear pair angles)

m<QNP = 180° - 66° (Substitution)

m<QNP = 114°

Next, find m<P

m<P = 180 - (m<QNP + m<PQN) (sum of ∆)

m<P = 180 - (114 + 33)

m<P = 180 - 147

m<P = 33°

Thus, in ∆QNP, there are two equal angles, namely, <P and <PQN.

An isosceles ∆ had two equal base angles. Therefore, ∆QNP must be an isosceles ∆.

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