after 3/4 of a minute a sloth has moved just 3/8 of a foot. what is the sloths speed in feet per minute

A simple random sample of size nequals10 is obtained from a population with muequals68 and sigmaequals15. (a) What must be true

valentina_108 [34]

Answer:

(a) The distribution of the sample mean ( $\bar x$ ) is N (68, 4.74²).

(b) The value of $P(\bar X$ is 0.7642.

(c) The value of $P(\bar X\geq 69.1)$ is 0.3670.

Step-by-step explanation:

A random sample of size n = 10 is selected from a population.

Let the population be made up of the random variable X.

The mean and standard deviation of X are:

$\mu=68\\\sigma=15$

(a)

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

Since the sample selected is not large, i.e. n = 10 < 30, for the distribution of the sample mean will be approximately normally distributed, the population from which the sample is selected must be normally distributed.

Then, the mean of the distribution of the sample mean is given by,

$\mu_{\bar x}=\mu=68$

And the standard deviation of the distribution of the sample mean is given by,

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{15}{\sqrt{10}}=4.74$

Thus, the distribution of the sample mean ( $\bar x$ ) is N (68, 4.74²).

(b)

Compute the value of $P(\bar X$ as follows:

$P(\bar X$

$=P(Z$

*Use a z-table for the probability.

Thus, the value of $P(\bar X$ is 0.7642.

(c)

Compute the value of $P(\bar X\geq 69.1)$ as follows:

Apply continuity correction as follows:

$P(\bar X\geq 69.1)=P(\bar X> 69.1+0.5)$

$=P(\bar X>69.6)$

$=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}>\frac{69.6-68}{4.74})$

$=P(Z>0.34)\\=1-P(Z$

Thus, the value of $P(\bar X\geq 69.1)$ is 0.3670.

7 0

3 years ago

Evaluate the expression for x=5

garri49 [273]

Answer:

There is not enough here to answer this problem

Step-by-step explanation:

Sorry : (

3 0

3 years ago

<img src="https://tex.z-dn.net/?f=e%5E%7B2x%7D%20%3D%20ln%205" id="TexFormula1" title="e^{2x} = ln 5" alt="e^{2x} = ln 5" align=

KiRa [710]

$e ^{2x} = ln5$

Solve for the real domain

$e ^{2x} = ln(5)$

if $f(x) =g(x),$ then $ln(f(x))= ln(g(x))$

$ln(e ^{2x} ) = ln(ln(5))$

Solve : $ln(e ^{2x} ) = ln(ln(5))$

use the logarithmic definition :

$ln(e^{f(x)} ) = f(x)$

$ln(e^{2x} ) = 2x$

$2x=ln(ln(5))$

Divide both sides by 2 :

$\frac{2x}{2} = \frac{ln(ln(5))}{2}$

$x= \frac{ln(ln(5))}{2}$

hope this helps!

8 0

3 years ago

Write an expression that has 2 as a coefficient. Explain how you know the 2 is a coefficient.

galina1969 [7]

Answer:

2x = 8

Step-by-step explanation:

2 is the coefficient because the coefficient always comes before the variable. In this case the variable is X, and 2 comes right before that signaling that it is (2)(x).

Hope this helps!

6 0

2 years ago

A turtle and a snail are 300 feet apart when they start moving towards each other. The turtle is moving at a speed of 5 feet per

choli [55]

Answer:

Step-by-step explanation:

velocity of turtle = 5 feet / min

velocity of snail = - 11 feet / min

By using the formula of relative velcoity

the velocity of turtle with respect to snail is

V' = velocity of turtle - velocity of snail

V' = 5 - (- 11)

V' = 16 feet / min

3 0

3 years ago