A manufacturer knows that their items have a normally distributed length, with a mean of 13.1 inches, and standard deviation of 4.1 inches. If 25 items are chosen at random, what is the probability that their mean length is less than 11.1 inches

Answers

Answer 1
Answer:

Answer:

0.73% probability that their mean length is less than 11.1 inches

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 = (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, which is also called standard error s = (\sigma)/(√(n))

In this problem, we have that:

\mu = 13.1, \sigma = 4.1, n = 25, s = (4.1)/(√(25)) = 0.82

What is the probability that their mean length is less than 11.1 inches

This is the pvalue of Z when X = 11.1. So

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

By the Central Limit Theorem

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

Z = (11.1 - 13.1)/(0.82)

Z = -2.44

Z = -2.44 has a pvalue of 0.0073.

0.73% probability that their mean length is less than 11.1 inches


Related Questions

What integer represents 5°F below zero
Laquita divides 3 pizzas equally among her 5 children how much pizza does each child receive
Do you think that students should be proficient in addition before learning multiplication?answer in 175 words! thank you so much :)
Will a truck that is 10 feet wide carrying a load that reaches 12 feet above the ground clear the semielliptical arch on the one-way road that passes under the bridge shown in the figure on the right? 13 ft --- 52 ft It will clear the arch because the height of the archway of the bridge 5 feet from the center is approximately (Round to two decimal places as needed.) feet.
If the legs of a right triangle measure 10 meters and 24 meters, how long is the hypotenuse?

If a function is defined by the formula y=1/2x + 3 and its domain is given by the set {-4,0,8}, then which of the following sets gives the function's range?

Answers

Answer:

y = {1, 3, 7}

Step-by-step explanation:

Given

y = ½x + 3

Domain: {-4, 0, 8}

Required

Determine the range of the function

To do this, we simply substitute each value of the domain in the given expression

We start with the first

Substitute -4 for x in y = ½x + 3

y = ½ * -4 + 3

y = -2 + 3

y = 1

Then 0

Substitute 0 for x in y = ½x + 3

y = ½ * 0 + 3

y = 0 + 3

y = 3

Lastly, 8

Substitute 8 for x in y = ½x + 3

y = ½ * 8 + 3

y = 4 + 3

y = 7

Hence, the range of the function is:

y = {1, 3, 7}

Answer:1,3,7

Step-by-step explanation:

how can you determine that the polynomial function does not have any zeros with even Multiplicity? Explain.​

Answers

Answer:

See Below.

Step-by-step explanation:

Remember multiplicity rules:

  • If a factor has an odd multiplicity (e.g. 1, 3, 5...), then the graph will cross the x-axis at that point.
  • If a factor has an even multiplicity (e.g. 2, 4, 6...), then the graph will bounce off the x-axis at that point.

From the graph, we can see that at our zeros, the graph always passes through the x-axis.

Hence, we do not have any zeros with even multiplicity since the graph does not "bounce" at any of the zeros.

Final answer:

To determine if a polynomial function has zeros with even multiplicity, examine the graph or the exponents of the factors in the function. If there are no real zeros or all the factors are raised to odd powers, there won't be any even multiplicity zeros.

Explanation:

In order to determine if a polynomial function has zeros with even multiplicity, we can examine the function's graph. If a polynomial function does not have any real zeros, then it does not have any zeros with even multiplicity. This is because even multiplicity zeros occur when a factor appears multiple times in the function. However, if all the factors are raised to odd powers, then there won't be any even multiplicity zeros. On the other hand, if the function does have real zeros, we can look at the graph of the function to check if any zeros occur with even multiplicity.

Learn more about Determining zeros of polynomial functions here:

brainly.com/question/11284559

#SPJ11

A set of data whose histogram is extremely skewed yields a sample mean and standard deviation of 69.5 and 10.75, respectively. What is the minimum percentage of observations that:A. are between 48 and 91.

and

B. are between 37.25 and 101.75

Answers

I am a beautiful person who can help you with the new one of those who are interested

13. Find the slope of any PLZ HELP!!!! 13. Find the slope of any line parallel to the line passing through (1,5) and (-1,0).a. 5/2
b. 2/5
c. -5/2
d. -5/2

Answers

Answer:

a

Step-by-step explanation:

5- 0 = 5

1- -1 = 2

5/2

The answer might be B. I’m not entirely sure.

Mrs.Montana has five students namely:rodley,cristina,christian,elsa and made .Count all the letters in each name.In which of the following sets the order of the names least to greatest.ARodley,cristina,Christian,mae,elsa
Bcristina,Christian elsa mae rodley
c Mae elsa rodley cristina Christian
D Christian Cristina rodley mae elsa

Answers

Answer:

C

Step-by-step explanation:

Mae, Elsa, Rodley, Cristina, Christian

Lysera enjoys exploring her land on horseback with its lush green valleys and ancient forests. She can cover a great deal of ground on her horse, Princess Grey Dawn, traveling at 9 km/h. Unfortunately Lysera has allergies. How far would Lysera and Princess Gray Dawn have moved while Lysera’s eyes were shut for 0.50 s during a hard sneeze? (answer in kilometers)

Answers

Answer:

0.00125 km.

Step-by-step explanation:

Given,

  • Speed of the horse on which princess travelling, v = 9km/h
  • Time taken by Lysera to sneeze = 0.5 s

As we know

     1 hour = 3600 seconds

=>\ 1\ second\ =\ (1)/(3600)\ hour

=>\ 0.50 second\ =\ (1)/(3600)* 0.50

                             =\ 1.38* 10^(-4)\ hour

So, time taken by Lysera to sneeze can be given by,

t\ =\ 1.38* 10^(-4)\ hour

According to definition of speed,

Speed\ =\ (distance)/(time)

=>distance = speed x time

                  =\ 9\ km/h* 1.38* 10^(-4)\ hour

                  = 0.00125 km

Hence, Princess Gray down will moved by 0.00125 km.