.4. What is the range of the data set?

214 83 106 99 83 155 175

Final answer:

140% of 15 is calculated by converting the percentage to a decimal (1.4) and then multiplying it by 15, giving a result of 21.

Explanation:

To determine 140% of 15, the process involves converting the percentage to a decimal and multiplying it by the given number. In the first step, 140% is transformed into 1.4 by dividing it by 100. Next, 15 is multiplied by 1.4. Executing this multiplication yields a final result of 21. The calculation follows a two-step procedure: conversion to a decimal and multiplication. This method ensures accurate determination of the desired percentage. In this case, the outcome of 140% of 15 is precisely 21, showcasing the systematic approach used in the mathematical computation.

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1. Mean (μ) of x' = 66, Standard Deviation (σx') = 2.

2. Shape tends towards normal with increasing sample size.

3. Z-scores: -1.2 for x' = 63.6, 1.6 for x' = 69.2.

4. Probabilities: P(x' ≥ 63.6) ≈ 0.8849, P(x' < 69.2) ≈ 0.9452, P(63.6 ≤ x' ≤ 69.2) ≈ 0.0603, P(x' > 69.2) ≈ 0.0548.

Let's break down each part of your question step by step:

1. Mean and Standard Deviation of the Sampling Distribution of x':

  The mean of the sampling distribution of the sample mean (x') is equal to the population mean (μ), which is 66 in this case.

  The standard deviation of the sampling distribution of the sample mean (x') is equal to the population standard deviation (σ) divided by the square root of the sample size (n). So:

  Standard Deviation of x' = σ / √n = 12 / √36 = 12 / 6 = 2

2. Shape of the Sampling Distribution of x':

  The shape of the sampling distribution of the sample mean (x') tends to follow a normal distribution, especially as the sample size increases. This is known as the Central Limit Theorem. The larger the sample size, the closer the sampling distribution resembles a normal distribution.

3. Z-Scores for x' = 63.6 and x' = 69.2:

  To calculate the z-scores, you can use the formula:

  Z = (X - μ) / (σ/√n)

  - For x' = 63.6:

    Z = (63.6 - 66) / (12/√36) = (-2.4) / (2) = -1.2

  - For x' = 69.2:

    Z = (69.2 - 66) / (12/√36) = (3.2) / (2) = 1.6

4. Probability Calculations:

  - P(x' ≥ 63.6): To find this probability, you can use a standard normal distribution table or calculator. P(Z ≥ -1.2) ≈ 0.8849 (rounded to 4 decimals).

  - P(x' < 69.2): Similarly, P(Z < 1.6) ≈ 0.9452 (rounded to 4 decimals).

  - P(63.6 ≤ x' ≤ 69.2): This is the difference between the two probabilities above: P(63.6 ≤ x' ≤ 69.2) ≈ 0.9452 - 0.8849 ≈ 0.0603 (rounded to 4 decimals).

5. There is a 60% chance that the value of x' is above (to 4 decimals):

  To find the probability that x' is above a certain value, you need to calculate P(x' > 69.2). You can use the complement rule:

  P(x' > 69.2) = 1 - P(x' < 69.2) ≈ 1 - 0.9452 ≈ 0.0548 (rounded to 4 decimals).

  So, there is a 5.48% chance (rounded to 4 decimals) that the value of x' is above 69.2.

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Answer:

μ = 66, σ = 2; The distribution is bell-shaped; Yes, this depends on the sample size; z = -1.2; z = 1.6; P(X ≥ 63.6) = 0.8849; P(X < 69.2) = 0.9452; P(63.6 ≤ X ≤ 69.2) = 0.8301; 65.5

Step-by-step explanation:

The central limit theorem states that if the sample size is greater than 30, the sample mean is roughly the same as the population mean.  This means it is 66.

The standard deviation of a sampling distribution of means is given by

σ/√n

For our data, this is

12/(√36) = 12/6 = 2

The central limit theorem states that the sampling distribution is approximately normal, so it will be bell-shaped.

The formula for the z score of a sampling distribution of means is

For the value of x = 63.6,

z = (63.6-66)/(12/(√36)) = -2.4/2 = -1.2

For the value of x = 69.2,

z = (69.2-66)/(12/(√36)) = 3.2/2 = 1.6

Using a z table, we see that the area under the curve to the left of z = -1.2 (for x = 63.6) is 0.1151.  However, we want P(x̄ ≥ 63.6); this means we want the area to the right.  We subtract our value from 1:

1-0.1151 = 0.8849

Using a z table, we see that the area under the curve to the left of z = 1.6 (for x = 69.2) is 0.9452.  This is P(x̄ < 69.2).

Since we have the area under the curve to the left of each endpoint, to find P(63.6 ≤ x̄ ≤ 69.2) we subtract these values:

0.9452-0.1151 = 0.8301

To find the value that would correspond in 60% of values being larger than, we first consider the fact that the z table gives us areas to the left of values, which is probabilities less than the value.  Our question is what number has a probability of 60% being larger than; this means we need to subtract from 1:

1-0.6 = 0.4

In a z table, we find the value as close to 0.4 as we can get.  This is 0.4013, which corresponds with a z score of -0.25.

Substituting this into our z formula, we have

Multiply both sides by 2:

2(-0.25) = ((X-66)/2)(2)

-0.5 = X-66

Add 66 to each side:

-0.5+66 = X-66+66

65.5 = X

Answer:

53.38

Step-by-step explanation:

Final answer:

The circumference of a circle with a radius of 17 inches can be calculated using the formula C=2πr. Substituting these values into the formula gives a circumference of approximately 106.76 inches.

Explanation:

The question is asking about the circumference of a circle, given its radius. The formula to find the circumference of a circle is C=2πr, where C is the circumference, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

In this case, the radius of the circle (r) is 17 inches. Substituting these values into the formula, we get:

C = 2 * 3.14 * 17 = 106.76 inches

So, "the circumference of the circle is approximately 106.76 inches".

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80%

Ummm bro the explanation is simple he keeps 8/10 and he saves 2/10 sooo

8/10 x 10 = 80/100 spends 80%

2/10 x 10 = 20/100 saves 20%

Easy peasy...

Final answer:

Glen saves $2 out of every $10 he earns, which is 20%. Therefore, he spends 80% of his earnings. That's the percentage of the money he gets to spend.

Explanation:

To figure out what percent of his earnings Glen gets to spend, you need to look at the portion that he is not required to save. If he earns $10 and is required to save $2, he gets to spend $7 out of every $10.

This means Glen gets to keep 80% of his earnings. The reasoning here is simple: for every $10, he saves $2 (which is 20% of $10) and the rest, which is $8, he gets to spend. Therefore, the percentage of his money that he gets to spend is $8/$10*100 which equals to 80%.

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