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shtirl [24]
3 years ago
13

Without doing any computation, decide which has a higher probability, assuming each sample is from a population that is normally

distributed with a mean equal to 100 and a standard deviation equal to 15. explain your reasoning. (a) p(90≤sample mean≤110) for a random sample of size n = 10 (b) p(90≤sample mean≤110) for a random sample of size n = 20
Mathematics
1 answer:
Nana76 [90]3 years ago
5 0
Answer: The probability in (b) has higher probability than the probability in (a).

Explanation:

Since we're computing for the probability of the sample mean, we consider the z-score and the standard deviation of the sampling distribution. Recall that the standard deviation of the sampling distribution approximately the quotient of the population standard deviation and the square root of the sample size.

So, if the sample size higher, the standard deviation of the sampling distribution is lower. Since the sample size in (b) is higher, the standard deviation of the sampling distribution in (b) is lower. 

Moreover, since the mean of the sampling distribution is the same as the population mean, the lower the standard deviation, the wider the range of z-scores. Because the standard deviation in (b) is lower, it has a wider range of z-scores.

Note that in a normal distribution, if the probability has wider range of z-scores, it has a higher probability. Therefore, the probability in (b) has higher probability than the probability in (a) because it has wider range of z-scores than the probability in (a).       
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Find the 67th term of the following arithmetic sequence.<br> 14, 20, 26, 32, ...
Jlenok [28]

Answer:

410

Step-by-step explanation:

You can use the equation f(n)= 14+(n-1)6 and you substitute in 67 for n.

7 0
2 years ago
25. John hired a plumber who charges a flat fee of $75 plus $55 per hour. The total charge
mestny [16]

Answer: 55x + 75 = 350; 5 hours

Step-by-step explanation:

What we know:

- A flat fee is $75

- John charges $55 an hour

- The total charge is $350

We need to write an equation to find how many hours John works.

<em>x </em>will represent hours worked.

55x + 75 = 350

We now need to solve for x.

Subtract 75 from both sides.

55x + 75 - 75 = 350 - 75

Simplify.

55x = 275

Divide 55 from both sides.

55x/55 = 275/55

Simplify.

x = 5

John worked 5 hours.

To check our work, we just plug in our x value!

55(5) + 75

275 + 75 = 350

3 0
2 years ago
The perimeter of a rectangle is 61 feet. The length is 5 more than twice the width. What is the length and width?
DochEvi [55]

Answer:

Length = 22 feet Width= 8.5 feet

Step-by-step explanation:

Perimeter= 61

Let Width= x

Length= 2x+5

Perimeter= 2l + 2w

61= 2(2x+5) + 2x

61 = 2(2x+5+x)

61/2 = 3x+5

30.5 -5 = 3x

25.5 = 3x

25.5/3 =x

x= 8.5

Hence, width = 8.5 feet

Then, the length = 2x+5 = 2(8.5) +5 = 22 feet

Hope this helps!

6 0
3 years ago
Select the correct infinitive.<br> ¿A dónde van Uds. los domingos?<br> _____ a la iglesia.
S_A_V [24]

Answer:

la respuesta es voy a la iglesia corona plis

6 0
2 years ago
When two six-sided dice are rolled, there are 36 possible outcomes. Find the probability that the sum is not 5.
zaharov [31]

Answer:

p(Not\ 5) = \frac{8}{9}

Step-by-step explanation:

Given:

Txo six-sided dice are rolled.

Total number of outcomes n(S) = 36

We need to find the probability that the sum is not equal to 5 p(Not 5).

Solution:

Using probability formula.

P(E)=\frac{n(E)}{n(S)}  ----------------(1)

Where:

n(E) is the number of outcomes favourable to E.

n(S) is the total number of equally likely outcomes.

The sum of two six-sided dice roll outcome is equal to 5 as.

Outcome as 5: {(1,4), (2,3), (3,2), (4,1)}

So, the total favourable events n(E) = 4

Now, we substitute n(E) and n(s) in equation 1.

P(5)=\frac{4}{36}

p(5) = \frac{1}{9}

Using formula.

p(Not\ E) + p(E) = 1

p(Not\ 5) + p(5) = 1

Now we substitute p(5) in above equation.

p(Not\ 5) + \frac{1}{9} = 1

p(Not\ 5) = 1-\frac{1}{9}

p(Not\ 5) = \frac{9-1}{9}

p(Not\ 5) = \frac{8}{9}

Therefore, the sum of two six-sided dice roll outcome is not equal to 5.

p(Not\ 5) = \frac{8}{9}

6 0
3 years ago
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