Explain how you can use a model to find 6x17

A process manufactures ball bearings with diameters that are normally distributed with mean 25.1 mm and standard deviation 0.08

marta [7]

Answer:

(a) The proportion of the diameters are less than 25.0 mm is 0.1056.

(b) The 10th percentile of the diameters is 24.99 mm.

(c) The ball bearing that has a diameter of 25.2 mm is at the 84th percentile.

(d) The proportion of the ball bearings meeting the specification is 0.8881.

Step-by-step explanation:

Let X = diameters of ball bearings.

The random variable X is normally distributed with mean, μ = 25.1 mm and standard deviation, σ = 0.08 mm.

To compute the probability of a Normally distributed random variable we need to first convert the raw scores to z-scores as follows:

z = (X - μ) ÷ σ

(a)

Compute the probability of X < 25.0 mm as follows:

P (X < 25.0) = P ((X - μ)/σ < (25.0-25.1)/0.08)

= P (Z < -1.25)

= 1 - P (Z < 1.25)

= 1 - 0.8944

= 0.1056

*Use a z-table for the probability.

Thus, the proportion of the diameters are less than 25.0 mm is 0.1056.

(b)

The 10th percentile implies that, P (X < x) = 0.10.

Compute the 10th percentile of the diameters as follows:

P (X < x) = 0.10

P ((X - μ)/σ < (x-25.1)/0.08) = 0.10

P (Z < z) = 0.10

z = -1.282

The value of x is:

z = (x - 25.1)/0.08

-1.282 = (x - 25.1)/0.08

x = 25.1 - (1.282 × 0.08)

= 24.99744

≈ 24.99

Thus, the 10th percentile of the diameters is 24.99 mm.

(c)

Compute the value of P (X < 25.2) as follows:

P (X < 25.2) = P ((X - μ)/σ < (25.2-25.1)/0.08)

= P (Z < 1.25)

= 0.8944

≈ 0.84

*Use a z-table for the probability.

Thus, the ball bearing that has a diameter of 25.2 mm is at the 84th percentile.

(d)

Compute the value of P (25.0 < X < 25.3) as follows:

P (25.0 < X < 25.3) = P ((25.0-25.1)/0.08 < (X - μ)/σ < (25.3-25.1)/0.08)

= P (-1.25 < Z < 2.50)

= P (Z < 2.50) - P (Z < -1.25)

= 0.99379 - 0.10565

= 0.88814

≈ 0.8881

*Use a z-table for the probability.

Thus, the proportion of the ball bearings meeting the specification is 0.8881.

4 0

3 years ago

Order the following numbers from least to greatest. 0.9 -2.4 -0.8 1.6 0.2

arlik [135]

1.6
0.9
0.2
-0.8
-2.4

Please give me brainliest!!!

5 0

4 years ago

Read 2 more answers

A school debate team has 4 girls and 6 boys. A total of 3 of the team members will be chosen to participate in the district deba

Varvara68 [4.7K]

The probability that 1 girl and 2 boys will be selected is given by:
$P(1\ boy,\ 2\ girls)=\frac{4C1\times6C2}{10C3}=\frac{1}{2}$
The correct answer choice is B. 1/2.

6 0

3 years ago

Read 2 more answers

Problem PageQuestion A circle has a radius of . Find the radian measure of the central angle that intercepts an arc of length .

notsponge [240]

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question.

A circle has a radius of 19m . Find the radian measure of the central angle θ that intercepts an arc of length 5m. Do not round any intermediate computations, and round your answer to the nearest tenth.

The formula for calculating the length of an arc $L = \frac{\theta}{360} * 2 \pi r$

θ is the central angle

r is the radius of the circle = 19m

L is the length of an arc = 5m

Substitute the given values into the formula and get the central angle θ

5 = θ/360 * 2(22/7)*19

5 = θ/2π * 119.4285714

θ/2π = 5/119.4285714

θ/2π = 0.041866

θ = 2π*0.041866

θ = 0.083732π

θ = 0.1π rad (to the nearest tenth)

Hence the radian measure of the central angle that intercepts an arc of length to the nearest tenth is 0.1π rad

8 0

3 years ago

Gary deposited $20 in a savings account earning 10% interest, compound annually. to the nearest cent, how much will he have in 3

Strike441 [17]

<h3>Answer: $26.62 </h3>

============================

Work Shown:

P = 20 is the amount deposited

r = 0.10 is the decimal form of the 10% interest rate

n = 1 means we compound 1 time per year (annually)

t = 3 is the number of years

Plug those four values into the compound interest formula below

A = P*(1+r/n)^(n*t)

A = 20*(1+0.1/1)^(1*3)

A = 20*(1+0.1)^(3)

A = 20*(1.1)^(3)

A = 20*1.331

A = 26.62

5 0

4 years ago

Read 2 more answers