Plz help i have i due by tomorrow

The time for a visitor to read health instructions on a Web site is approximately normally distributed with a mean of 10 minutes

klio [65]

Answer:

a) The mean is 10 and the variance is 0.0625.

b) 0.6826 = 68.26% probability that the mean time of the visitors is within 15 seconds of 10 minutes.

c) 10.58 minutes.

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 normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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.

Normally distributed with a mean of 10 minutes and a standard deviation of 2 minutes.

This means that $\mu = 10, \sigma = 2$

Suppose 64 visitors independently view the site.

This means that $n = 64, = \frac{2}{\sqrt{64}} = 0.25$

a. The expected value and the variance of the mean time of the visitors.

Using the Central Limit Theorem, mean of 10 and variance of (0.25)^2 = 0.0625.

b. The probability that the mean time of the visitors is within 15 seconds of 10 minutes.

15 seconds = 15/60 = 0.25 minutes, so between 9.75 and 10.25 seconds, which is the p-value of Z when X = 10.25 subtracted by the p-value of Z when X = 9.75.

X = 10.25

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

By the Central Limit Theorem

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

$Z = \frac{10.25 - 10}{0.25}$

$Z = 1$

$Z = 1$ has a p-value of 0.8413.

X = 9.75

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

$Z = \frac{9.75 - 10}{0.25}$

$Z = -1$

$Z = -1$ has a p-value of 0.1587.

0.8413 - 0.1587 = 0.6826.

0.6826 = 68.26% probability that the mean time of the visitors is within 15 seconds of 10 minutes.

c. The value exceeded by the mean time of the visitors with probability 0.01.

The 100 - 1 = 99th percentile, which is X when Z has a p-value of 0.99, so X when Z = 2.327.

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

$2.327 = \frac{X - 10}{0.25}$

$X - 10 = 2.327*0.25$

$X = 10.58$

So 10.58 minutes.

6 0

3 years ago

PLEASE HELP 20 POINTS IF YOU HELP AND WILL BE MRAKED BRAINLEST!!!!!!!!!!!!!!!!The two-way table below shows the number of studen

Yuliya22 [10]

Your answer is the last option, 6.

We can work this out by looking for the total of people that like tennis in the table, and subtracting it from the total amount of people that like baseball.

This gives us a total of 46 people that like baseball, subtract 40 people that like tennis, and 46 - 40 = 6.

I hope this helps!

3 0

3 years ago

Z

timofeeve [1]

Answer:

Z

ㄲ

Respuesta: se necesitan 15 casos para las 4 lámincis.

El primer 3 indica los 3 clavos para el lado izquierdo de la primera lámina. los números del L...4

indican el número de laminas, y el segundo 3 indica el número de claves para el lado derecho de

cada lamina.

lámina y se calcula

A mumero de casos se obtiene relacionando el número de liminas con la cantidad de clavos per

3 + nuncro deliminas) X 3

Cuilice si patria numérico anterior para encontrar la cantidad de clavos necesarios según el número

b. 6 laminas

10 Sáminas

0.

-se de forma física bien identificados.

5: Leer el contenido de la presente guía, realizar las

FECHA: 06 al 17 septiembre 2021

Tercel CUMP

E de liminas

a

Liminas

C.

8 0

3 years ago

What is the value of c such that the line y=2x+3 is tangent to the parabola y=cx^2

satela [25.4K]

The value of $c$ such that the line $y = 2\cdot x + 3$ is tangent to the parabola $y = c\cdot x^{2}$ is $-\frac{1}{3}$ .

If $y = 2\cdot x + 3$ is a line <em>tangent</em> to the parabola $y = c\cdot x^{2}$ , then we must observe the following condition, that is, the slope of the line is equal to the <em>first</em> derivative of the parabola:

$2\cdot c \cdot x = 2$ (1)