HELPPPPPPP !!! I need the answer in less than 5 minutes!!!

A tablet PC contains 3217 music files. The distribution of file size is highly skewed with many small file sizes. The mean file

Law Incorporation [45]

Answer:

a) 23.89% probability that the average size of 30 randomly selected music files taken from the tablet is less than 1.93 MB

b) 35.57% probability that the average size of 50 randomly selected music files taken from the tablet is more than 2.52 MB

c) At least 87 files

Step-by-step explanation:

To solve this question, we need 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:

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

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:

$\mu = 2.35, \sigma = 3.25$

a. What is the probability that the average size of 30 randomly selected music files taken from the tablet is less than 1.93 MB?

$n = 30, s = \frac{3.25}{\sqrt{30}} = 0.59$

This probability is the pvalue of Z when X = 1.93. So

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

By the Central Limit Theorem

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

$Z = \frac{1.93 - 2.35}{0.59}$

$Z = -0.71$

$Z = -0.71$ has a pvalue of 0.2389

23.89% probability that the average size of 30 randomly selected music files taken from the tablet is less than 1.93 MB

b. What is the probability that the average size of 50 randomly selected music files taken from the tablet is more than 2.52 MB?

$n = 50, s = \frac{3.25}{\sqrt{50}} = 0.46$

This pobability is 1 subtracted by the pvalue of Z when X = 2.52.

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

$Z = \frac{2.52 - 2.35}{0.46}$

$Z = 0.37$

$Z = 0.37$ has a pvalue of 0.6443

1 - 0.6443 = 0.3557

35.57% probability that the average size of 50 randomly selected music files taken from the tablet is more than 2.52 MB

c. How many files would you need to sample if you wanted the standard deviation of the sample mean size to lie no larger than 0.35 MB?

At least n files, in which n is found when s = 0.35. So

$s = \frac{3.25}{\sqrt{n}}$

$0.35 = \frac{3.25}{\sqrt{n}}$

$0.35\sqrt{n} = 3.25$

$\sqrt{n} = \frac{3.25}{0.35}$

$(\sqrt{n})^{2} = (\frac{3.25}{0.35})^{2}$

$n = 86.2$

Rounding up

We would need at least 87 files.

6 0

4 years ago

Find the vertex of the following quadratic function f(x)=x^2+2x+1

Usimov [2.4K]

Answer:

The answer is that the vertex is: (1, 0)

Step-by-step explanation:

Use the "Completing the Square Method":

(x - h)^2 - k = 0, the vertex is (h, -k)

Complete the square:

x^2 + 2x + 1 = 0

x^2 + 2x = -1

(2/2)^2 = 1, add 1 to both sides of the equation.

x^2 + 2x + 1 = -1 + 1

(x + 1)^2 = 0

(x + 1)^2 - 0 = 0 (Just to put a placeholder in for he -k)

The vertex is (1, 0)

3 0

4 years ago

7. You have been hired by a company to write a report on Internet companies’ Wi-Fi ranges. They have requested that all values b

Anit [1.1K]

Answer: what is the question asking?

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Working together , 5 friends collected 40 5/8 bags of food for the homeless . On a average how many bags of food did each friend

natima [27]

8.125. Just divide the number of bags they collected together.by how many of them collected them, to find out how many each of them collected

8 0

3 years ago

Read 2 more answers

Gabrielle is cutting a triangular sign with a base of 8 inches. The perpendicular distance from the base of the sign to its vert

kkurt [141]

The area of the triangular sign is 36 square inches, if Gabrielle is cutting a triangular sign with a base of 8 inches and the perpendicular distance from the base of the sign to its vertex is 9 inches.

Step-by-step explanation:

The given is,

Gabrielle is cutting a triangular sign

Base of 8 inches

The perpendicular distance from the base of the sign to its vertex is 9 inches

Step:1

Formula for area of triangle is,

Area, $A = \frac{bh}{2}$ .....................................(1)

Where, b - Base of triangle

h - Height of triangle

From given value,

b - 8 inches

h - 9

Equation (1) becomes,

$A = \frac{(8)(9)}{2}$

$=\frac{72}{2}$

= 36

Area of triangle sign, A = 36 square inches

Result:

The area of the triangular sign is 36 square inches, if Gabrielle is cutting a triangular sign with a base of 8 inches and the perpendicular distance from the base of the sign to its vertex is 9 inches.

8 0

3 years ago