Someone help and plz make sure it’s right plz! :)

A manufacturing process is designed to produce bolts with a 0.75-inch diameter. Once each day, a random sample of 36 bolts is se

larisa [96]

Answer:

0.0026 = 0.26% probability that the manufacturing line will be shut down unnecessarily

Step-by-step explanation:

We need to understand the normal probability distribution and the central limit theorem to solve this question.

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 normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 0.75, \sigma = 0.04, n = 36, s = \frac{0.04}{\sqrt{36}} = 0.0067$

What is the probability that the manufacturing line will be shut down unnecessarily?

Less than 0.73 or more than 0.77.

Less than 0.73

pvalue of Z when X = 0.73

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

By the Central Limit Theorem

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

$Z = \frac{0.73 - 0.75}{0.0067}$

$Z = -3$

$Z = -3$ has a pvalue of 0.0013

More than 0.77

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

$Z = \frac{0.77 - 0.75}{0.0067}$

$Z = 3$

$Z = 3$ has a pvalue of 0.9987

1 - 0.9987 = 0.0013

2*0.0013 = 0.0026

0.0026 = 0.26% probability that the manufacturing line will be shut down unnecessarily

3 0

3 years ago

An airline charges the following baggage fees: $25 for the first bag and $35 for the second. Suppose 51% of passengers have no c

Orlov [11]

Answer:

The average revenue per passenger is about $13.85

μ = $13.85

The corresponding standard deviation is $14.51

σ = $14.51

The airline should expect revenue of $1,662 with a standard deviation of $14.51 for a flight of 120 passengers.

Expected revenue = $1,662 ± 14.51

Step-by-step explanation:

An airline charges the following baggage fees:

$25 for the first bag and $35 for the second

Suppose 51% of passengers have no checked luggage,

P(0) = 0.51

33% have one piece of checked luggage and 16% have two pieces.

P(1) = 0.33

P(2) = 0.16

a. Build a probability model, compute the average revenue per passenger, and compute the corresponding standard deviation.

The average revenue per passenger is given by

μ = 0×P(0) + 25×P(1) + 35×P(2)

μ = 0×0.51 + 25×0.33 + 35×0.16

μ = 0 + 8.25 + 5.6

μ = $13.85

Therefore, the average revenue per passenger is about $13.85

The corresponding standard deviation is given by

σ = √σ²

Where σ² is the variance and is given by

σ² = (0 - 13.85)²×0.51 + (25 - 13.85)²×0.33 + (35 - 13.85)²×0.16

σ² = 97.83 + 41.03 + 71.57

σ² = 210.43

So,

σ = √210.43

σ = $14.51

Therefore, the corresponding standard deviation is $14.51

b. About how much revenue should the airline expect for a flight of 120 passengers? With what standard deviation?

For 120 passengers,

Expected revenue = 120×$13.85

Expected revenue = $1,662 ± 14.51

Therefore, the airline should expect revenue of $1,662 with a standard deviation of $14.51 for a flight of 120 passengers.

6 0

2 years ago

1. Which of the following is true regarding the graph of y = 1/x ?

KATRIN_1 [288]

Answer:

b. There are horizontal and vertical asymptotes

Step-by-step explanation:

The graph is a hyperbola with asymptotes of x=0 and y=0

7 0

3 years ago

Factor the expression 8a + 16c

Stella [2.4K]

The answer for this question is 80

3 0

3 years ago

Read 2 more answers

Please help me out! I tried to do it but I got it wrong.

Anika [276]

This may or may not be right.

You know that they are a graduate, and the total number of graduates are 2610.

The amount of graduates receiving financial aid is 1879.

The probability that a graduate student is on financial aid is: 1879/2610 = 0.7199 or 72%

4 0

3 years ago