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marishachu [46]
3 years ago
11

Find the population variance and standard deviation. 8​, 17​, 29​, 35​, 41 Choose the correct answer below. Fill in the

answer box to complete your choice.
a. sigma^2 =
b. s^2 =
Mathematics
1 answer:
Nuetrik [128]3 years ago
7 0

Answer:

(a) σ²  = 144

(b) s² = 12

Step-by-step explanation:

(a) Population variance σ² = ∑(X - \overline{X})² / N

The arithmetic mean \overline{X} = \frac{8 + 17 + 29 + 35 + 41}{5}

                                   \overline{X} = \frac{130}{5}

                                   \overline{X} = 26

σ²  =  \frac{(8 - 26)^{2} + (17 - 26)^{2} + (29 - 26)^{2} + (35 - 26)^{2} + (41 - 26)^{2}}{5}

     =  \frac{(- 18)^{2} + (- 9)^{2} + (3)^{2} + (9)^{2} + (15)^{2}}{5}

     =  \frac{324\ +\ 81\ +\ 9\ +\ 81\ +\ 225}{5}

     = \frac{720}{4}

σ²  = 144

(b) Standard\ deviation = \sqrt{Variance}

                                   = \sqrt{144}

                                   = 12

 

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VashaNatasha [74]
147 3/10
basically 147 and then 3 over 10
6 0
3 years ago
Read 2 more answers
True or false: an cubic function may have 3 irrational zeros
jolli1 [7]
<h3>Answer: True</h3>

The key word here is "may" meaning that we could easily have 3 rational roots as well. An example of a cubic having 3 irrational roots would be

(x-1)(x-2)(x-3) = x³ - 6x² + 11x - 6

This has the rational roots x = 1, x = 2, x = 3.

However, we could easily replace 1,2,3 with any irrational numbers we want. So that's why the statement "a cubic has three irrational roots" is sometimes true.

In some cases, a cubic may only have 1 real root and the other 2 roots are imaginary.

3 0
3 years ago
((I will give brainy and 20 points to the first person who answers correctly!))
masya89 [10]
1. We don't know the meaning of "{There is a box image here}".

If you're dealing with congruent figures, match the corresponding letters in the name of the figure:
.. E F G H
.. Q R S T
If you're concerned with QT (1st and 4th letters), you need to look at EH (1st and 4th letters).

If EFGH ≅ QRST, then QT = EH = 6.3.


2. LM = ST = 5.2
4 0
3 years ago
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 5.5 years, and standard deviation of
Alina [70]

Answer:

If 24 items are picked at random, 8% of the time their mean life will be less than 5.156 years.

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore 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 pvalue, 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 random variable X, with mean \mu and standard deviation \sigma, the sample means with size n of at least 30 can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 5.5, \sigma = 1.2, n = 24, s = \frac{1.2}{\sqrt{24}} = 0.2449

If 24 items are picked at random, 8% of the time their mean life will be less than how many years?

This is the value of X when Z has a pvalue of 0.08. So it is X when Z = -1.405.

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

By the Central Limit Theorem

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

-1.405 = \frac{X - 5.5}{0.2449}

X - 5.5 = -1.405*0.2449

X = 5.156

If 24 items are picked at random, 8% of the time their mean life will be less than 5.156 years.

3 0
3 years ago
PLEASE HELP I NEED THIS FAST
iren2701 [21]

Answer:

Step-by-step explanation: the x side is +5 and the y side is -15

3 0
3 years ago
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