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3 years ago

Question

Mathematics

2 answers:

weeeeeb [17]3 years ago

8 0

Answer:

ln(2) - ln(7)

Step-by-step explanation:

Nadusha1986 [10]3 years ago

5 0

Answer:

ln(2)-ln(7)

Step-by-step explanation:

You might be interested in

For the base b of a logarithmic function, b>0 and b≠1 True False

STatiana [176]

True cus i don’t remember but it’s true

4 0

2 years ago

The Office of Student Services at a large western state university maintains information on the study habits of its full-time st

Vera_Pavlovna [14]

Answer:

0.8254 = 82.54% probability that the mean of this sample is between 19.25 hours and 21.0 hours

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 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.

Mean of 20 hours, standard deviation of 6:

This means that $\mu = 20, \sigma = 6$

Sample of 150:

This means that $n = 150, s = \frac{6}{\sqrt{150}}$

What is the probability that the mean of this sample is between 19.25 hours and 21.0 hours?

This is the p-value of Z when X = 21 subtracted by the p-value of Z when X = 19.5. So

X = 21

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

By the Central Limit Theorem

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

$Z = \frac{21 - 20}{\frac{6}{\sqrt{150}}}$

$Z = 2.04$

$Z = 2.04$ has a p-value of 0.9793

X = 19.5

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

$Z = \frac{19.5 - 20}{\frac{6}{\sqrt{150}}}$

$Z = -1.02$

$Z = -1.02$ has a p-value of 0.1539

0.9793 - 0.1539 = 0.8254

0.8254 = 82.54% probability that the mean of this sample is between 19.25 hours and 21.0 hours

3 0

3 years ago

HELPPP PLEASE!!! IM BEING TIMED!!!

Elena-2011 [213]

Answer:

y=2x+4

Step-by-step explanation:

8=2(6)+b

8=12+b

4=b

5 0

2 years ago

A special deck of cards has ten cards. Four are green (G), four are blue (B), and two are red (R). When a card is picked, the co

a_sh-v [17]

Answer:

{GT, GH, BT, BH, RT, RH};

1 /5;

Mutually exclusive ;

Not mutually exclusive.

Step-by-step explanation:

Given :

Green cards, G = 4

Blue cards, B = 4

Red cards, R = 2

For a coin toss :

{H, T}

A card is picked, then a coin is tossed :

Sample space :

{GT, GH, BT, BH, RT, RH}

2.) probability of picking a green card, then probability of landing a head on a coin toss

P(A) = number of required outcome / Total possible outcomes

P(A) = P(green card) * P(Head)

P(A) = (4 / 10) * (1/2)

P(A) = 4 /20

P(A) = 1/5

C.)

Both A and B are mutually exclusive, since both event A and event B cannot occur together, since both red and green cannot be picked during a single pick, this either a red is picked or green is picked, then they are A and B are mutually exclusive.

D.) Event A and C are not mutually exclusive, picking a green card, event A and picking a red or blue card, event B. Both event can happen simultaneously, hence, event A and B are not mutually exclusive.

6 0

3 years ago

Erin cooked 5

frutty [35]

Answer:

Addition

Step-by-step explanation:

I'm not sure if the numbers are tog or not

8 0

2 years ago