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storchak [24]
3 years ago
5

Suppose the parent population has an exponential distribution with a mean of 15 and standard deviation of 12. Use the Central Li

mit Theorem to describe the distribution of when drawing samples of size 30.
Mathematics
1 answer:
bazaltina [42]3 years ago
4 0

Answer:

The sampling distribution of the sample mean of size 30 will be approximately normal with mean 15 and standard deviation 2.19.

Step-by-step explanation:

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.

For the population, we have that:

Mean = 15

Standard deviaiton = 12

Sample of 30

By the Central Limit Theorem

Mean 15

Standard deviation s = \frac{12}{\sqrt{30}} = 2.19

Approximately normal

The sampling distribution of the sample mean of size 30 will be approximately normal with mean 15 and standard deviation 2.19.

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The first term of a geometric sequence is 7, and the ratio (multiplier) is 3. what is the sum of the first 5 terms of the sequen
Anni [7]
Hello,

1)
a_{1}=7
a_{2}=7*3
a_{3}=7*3^2

a_{n}=7*3^{n-1}

s=a_{1}+a_{2}+a_{3}+a_{4}+a_{5}=7*(1+3^1+3^2+3^3+3^4)
=7*\frac{3^{5}-1}{3-1}
=7*242/2=847

2)
b_{8}=6*8^{8-1}=12582912




















4 0
3 years ago
What is the slope of the line that passes through the following points:<br> (4, -3), (-5, 10)
umka21 [38]

Answer:

-9/13

Step-by-step explanation:

The formula for slope is [ y2-y1/x2-x1 ].

10-(-3)/-5-4

13/-9

-9/13

Best of Luck!

5 0
3 years ago
Your school football team has 10 scheduled games for the season. You want to attend at least 4 games. How many different combina
viva [34]

24 combinations i believe

8 0
3 years ago
Given that tan θ ≈ 1.072, where 0 &lt; θ &lt; , 2 π find the values of sin θ and cos θ.
anygoal [31]

Answer:

The answer to your question is

sin Ф = 0.731 and sinФ = -0.731; cos Ф 0.682 and cos Ф = -0.682

Step-by-step explanation:

tan Ф = 1.072,  0 < Ф < 2 π,   tan Ф is positive, find the solution in the first and third quadrangle.

- tan Ф = opposite side / adjacent side

- 1.072 / 1 = opposite side / adjacent side

- opposite side = 1.072 and adjacent side = 1

  Calculate hypotenuse

  c² = a² + b²

  c² = 1.072² + 1²

  c² = 2.149

  hypotenuse = c = 1.466

First quadrangle

  sin Ф = 1.072 / 1.466 = 0.731

  cos Ф = 1 / 1.466 = 0.682

Third quadrangle

  sin Ф = -1.072 / 1.466 = -0.731

  cos Ф = -1 / 1.466 = -0.682

5 0
3 years ago
Evaluate the polynomial when a.x=0 and b.x=-1<br> x2 – 3x - 7
Arlecino [84]

Answer:

a) -7 & b) -6

Step-by-step explanation:

Here,

a) x = 0

Solution ↦

x2 - 3x - 7 \\  =  0 \times 2 - 3 \times 0 - 7 \\  =  - 7

b) x = -1

Solution ↦

x2 - 3x - 7 \\  =  - 1 \times 2 - 3 \times ( - 1) - 7 \\  =  - 2 + 3 - 7 \\  =  - 9 + 3 \\  =  - 6

6 0
3 years ago
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