C. 121.73

A particular variety of watermelon weighs on average 20.4 pounds with a standard deviation of 1.23 pounds. Consider the sample m

love history [14]

Answer:

a) The expected value of the sample mean weight is 20.4 pounds.

b)The standard deviation of the sample mean weight is 0.123.

c) There is a 14.46% probability the sample mean weight will be less than 20.27.

d) This value is $c = 20.6153$ .

Step-by-step explanation:

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 $\frac{\sigma}{\sqrt{n}}$ .

Problems of normally distributed samples can be 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.

In this problem, we have that:

A particular variety of watermelon weighs on average 20.4 pounds with a standard deviation of 1.23 pounds. This means that $\mu = 20.4, \sigma = 1.23$

Consider the sample mean weight of 100 watermelons of this variety. This means that $n = 100$ .

a. What is the expected value of the sample mean weight? Give an exact answer.

By the Central Limit Theorem, it is the same as the mean of the population. So the expected value of the sample mean weight is 20.4 pounds.

b. What is the standard deviation of the sample mean weight? Give your answer to four decimal places.

By the Central Limit Theorem, that is:

$s = \frac{\sigma}{\sqrt{n}} = \frac{1.23}{\sqrt{100}} = 0.123$

The standard deviation of the sample mean weight is 0.123.

c. What is the approximate probability the sample mean weight will be less than 20.27?

This is the pvalue of Z when $X = 20.27$ .

Since we are working with the sample mean, we use $s$ instead of $\sigma$ in the Z score formula

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

$Z = \frac{20.27 - 20.4}{0.123}$

$Z = -1.06$

$Z = -1.06$ has a pvalue of 0.1446.

This means that there is a 14.46% probability the sample mean weight will be less than 20.27.

d. What is the value c such that the approximate probability the sample mean will be less than c is 0.96?

This is the value of $X = c$ that is in the 96th percentile, that is, it's Z score has a pvalue 0.96.

So we use $Z = 1.75$

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

$1.75 = \frac{c - 20.4}{0.123}$

$c - 20.4 = 0.123*1.75$

$c = 20.6153$

This value is $c = 20.6153$ .

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2 years ago

Kareem lives 4/10 of a mile from the mall. Write twp equivalent fractions that show what fraction of a mile Kareem lives from th

Vadim26 [7]

Answer:

Step-by-step explanation:

4/10 can be written in several different ways:

2/5, 40/100 (same as 0.4).

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3 years ago

ANYONE GOOD AT MATH?<br><br> PLEASE PLEASE PLEASE SOMEONE HELP ME :(

Mumz [18]

Answer:

The parent function is $f(x)=a(x-h)^{2} +k$

That Parabola's equation is $f(x)=x^{2}$

Step-by-step explanation:

I can't really explain much, but the top equation is a formula for <em>all </em>equations for a parabola. h and k are the x and y-values of the vertex. a is, well, a.

How did I find the equation of the parabola? Simple. Since the vertex is on the origin, h and k are 0. Also, because it intercepts (2,4) and (1,1), a=1.

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When graphed, which parabola opens downward? y = –3x2 y = (x – 3)2 y = x2 – 3

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The answer to this question is y = –3x^2, just had this on e2020 :)

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3 years ago

Read 2 more answers

A pizza is to be cut into halves. Each of these halves is to be cut into sevenths. What fraction of the pizza is each of the fin

Hitman42 [59]

Answer: $\dfrac{1}{14}$

Step-by-step explanation:

Given, A pizza is to be cut into halves.

Since half is represented by $\dfrac12$ .

So each piece is now $\dfrac12$ of the original.

if each of these halves is to be cut into sevenths, then the fraction of final pieces would be: $\dfrac{1}{2}\times\dfrac{1}{7}=\dfrac{1}{14}$ or we can say each half is divides into 7 pieces since there are two halves, so there will be 2 x 7 = 14 peices.

And the fraction of the pizza is each of the final pieces = $\dfrac{1}{14}$ .

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3 years ago