Please awnser my other question

The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.7 millimeters and a standard deviati

slava [35]

Answer:

The diameter that separates the top 3% is of 5.85 millimeters, and the one which separates the bottom 3% is of 5.55 millimeters.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Mean of 5.7 millimeters and a standard deviation of 0.08 millimeters.

This means that $\mu = 5.7, \sigma = 0.08$

Top 3%

The 100 - 3 = 97th percentile, which is X when Z has a p-value of 0.97, so X when Z = 1.88.

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

$1.88 = \frac{X - 5.7}{0.08}$

$X - 5.7 = 1.88*0.08$

$X = 5.85$

Bottom 3%

The 3rd percentile, which is X when Z has a p-value of 0.03, so X when Z = -1.88.

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

$-1.88 = \frac{X - 5.7}{0.08}$

$X - 5.7 = -1.88*0.08$

$X = 5.55$

The diameter that separates the top 3% is of 5.85 millimeters, and the one which separates the bottom 3% is of 5.55 millimeters.

7 0

3 years ago

Two friends sold many pieces of furniture and made $1550 during their garage sale. They had fifteen more $10 bills than $50 b

Novosadov [1.4K]

Answer:

The number of $ 10 bills is 37, the number of $ 20 is 6 and the number of $ 50 bills is 22.

Step-by-step explanation:

Let n₁ = number of $ 10 bills,

Let n₂ = number of $ 20 bills and

Let n₃ = number of $ 50 bills

Given that 10n₁ + 20n₂ + 50n₃ = 1550 (1)

Also, since we have fifteen more $10 bills than $50 bills, n₁ = n₃ + 15 (2)

and we have 4 more than three times as many $20 bills as $50 bills. n₃ = 3n₂ + 4. (3)

substituting equations (2) and (3) into (1), we have

10(n₃ + 15) + 20n₂ + 50n₃ = 1550

expanding the bracket, we have

10n₃ + 150 + 20n₂ + 50n₃ = 1550

collecting like terms, we have

60n₃ + 150 + 20n₂ = 1550

inserting equation (3), we have

60(3n₂ + 4) + 150 + 20n₂ = 1550

expanding the bracket, we have

180n₂ + 240 + 150 + 20n₂ = 1550

collecting like terms, we have

200n₂ + 390 = 1550

subtracting 390 from both sides, we have

200n₂ = 1550 - 390

200n₂ = 1160

dividing both sides by 200, we have

n₂ = 1160/200

n₂ = 5.8

n₂ ≅ 6 since it cannot be a fraction.

Substituting this into (3), we have

n₃ = 3n₂ + 4 = 3(6) + 4 = 18 + 4 = 22

substituting n₃ into (2), we have

n₁ = n₃ + 15 = 22 + 15 = 37

So, the number of $ 10 bills is 37, the number of $ 20 is 6 and the number of $ 50 bills is 22.

3 0

3 years ago

Need help plz don't understand

antiseptic1488 [7]

48, because 8×6=48. Each touchdown is 6 points and there are 8 touchdowns, so you would multiply.

4 0

3 years ago

How many goths of a bulletin board will each student decorate

sweet [91]

Answer:

by dividing the fraction with multipication

Step-by-step explanation:

solve the fraction using division and multipication

7 0

3 years ago

A cow is tied with a rope of length 14 m at the corner of a rectangle field of dimension 20 m × 16 m, then the area of the fiel

Paha777 [63]

Anwser

D) 160

Step by step explanation

To find the area of a object you must multiply the length by the height in this case they gave you an equation instead of an exact height so the first thing you have to do is:

20m x 16m = 320m

But as you can see, all of the answers have an exponent of two meaning we would have to divide 320 by 2

320 ÷ 2 = 160

Brainliest?

8 0

3 years ago