What decimal part of 36 is 20.88?? (Someone please answer quick)

The mean life of a television set is 119 months with a standard deviation of 14 months. If a sample of 74 televisions is randoml

irina [24]

Answer:

50.34% probability that the sample mean would differ from the true mean by less than 1.1 months

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 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:

$\mu = 119, \sigma = 14, n = 74, s = \frac{14}{\sqrt{74}} = 1.63$

If a sample of 74 televisions is randomly selected, what is the probability that the sample mean would differ from the true mean by less than 1.1 months

This is the pvalue of Z when X = 119 + 1.1 = 120.1 subtracted by the pvalue of Z when X = 119 - 1.1 = 117.9. So

X = 120.1

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

By the Central Limit Theorem

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

$Z = \frac{120.1 - 119}{1.63}$

$Z = 0.68$

$Z = 0.68$ has a pvalue of 0.7517

X = 117.9

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

$Z = \frac{117.9 - 119}{1.63}$

$Z = -0.68$

$Z = -0.68$ has a pvalue of 0.2483

0.7517 - 0.2483 = 0.5034

50.34% probability that the sample mean would differ from the true mean by less than 1.1 months

8 0

3 years ago

#1

Ksivusya [100]

Answer:

= 188, x = 7.89, s = 2.23

Step-by-step explanation:

= 188, x = 7.89, s = 2.23

3 0

2 years ago

Solve for x:<br> 2(3x + 4) + 2 = 4 + 3x

Anton [14]

Answer:

-2

Step-by-step explanation:

Distribute

2

(

3

+

4

)

+

2

=

4

+

3

{\color{#c92786}{2(3x+4)}}+2=4+3x

2(3x+4)+2=4+3x

6

+

8

+

2

=

4

+

3

{\color{#c92786}{6x+8}}+2=4+3x

6x+8+2=4+3x

2

Add the numbers

6

+

8

+

2

=

4

+

3

6x+{\color{#c92786}{8}}+{\color{#c92786}{2}}=4+3x

6x+8+2=4+3x

6

+

1

0

=

4

+

3

6x+{\color{#c92786}{10}}=4+3x

6x+10=4+3x

3

Rearrange terms

6

+

1

0

=

4

+

3

6x+10={\color{#c92786}{4+3x}}

6x+10=4+3x

6

+

1

0

=

3

+

4

6x+10={\color{#c92786}{3x+4}}

6x+10=3x+4

4

Subtract

1

0

10

from both sides of the equation

6

+

1

0

=

3

+

4

6x+10=3x+4

6

+

1

0

−

1

0

=

3

+

4

−

1

0

6x+10{\color{#c92786}{-10}}=3x+4{\color{#c92786}{-10}}

6x+10−10=3x+4−10

5

Simplify

Subtract the numbers

6

=

3

−

6

6x=3x-6

6x=3x−6

6

Subtract

3

3x

from both sides of the equation

6

=

3

−

6

6x=3x-6

6x=3x−6

6

−

3

=

3

−

6

−

3

6x{\color{#c92786}{-3x}}=3x-6{\color{#c92786}{-3x}}

6x−3x=3x−6−3x

7

Simplify

Combine like terms

3

=

−

6

3x=-6

3x=−6

8

Divide both sides of the equation by the same term

3

=

−

6

3x=-6

3x=−6

3

=

−

6

3

\frac{3x}{{\color{#c92786}{3}}}=\frac{-6}{{\color{#c92786}{3}}}

33x=3−6

9

Simplify

Cancel terms that are in both the numerator and denominator

Divide the numbers

=

−

2

3 0

3 years ago

Read 2 more answers

A manufacturing company produces valves in various sizes and shapes. One particular valve plate is supposed to have a tensile st

ss7ja [257]

Answer:

Step-by-step explanation:

Hello!

The researcher wants to test if the valve plates manufactured have the expected tensile strength of 5 lbs/mm. So he took a sample of 42 valve plates and measured their tensile strength, obtaining a sample mean of X[bar]= 5.0611 lbs/mm and a sample standard deviation of S=0.2803 lbs/mm.

The study variable is:

X: tensile strength of a valve plate (lbs/mm)

The parameter of interest is the mean tensile strength of the valve plates, μ.

If the claim is that the valve plates of the sample have on average tensile strength of 5 lbs/mm, symbolically: μ = 5

a) The statistic hypotheses are:

H₀: μ = 5

H₁: μ ≠ 5

b) To determine the critical values and rejection region of a hypothesis test you need three to determine three factors of the hypothesis test:

1) The statistical hypothesis.

2) The significance level.

3) The statistic to use for the analysis.

The statistic hypothesis determines the number of critical values and the direction of the rejection region, in this case, the test is two-tailed you will have two critical values and the rejection region will be divided into two.

With the statistic, you will determine the distribution under which you will work and the significance level determines the probability of rejecting the null hypothesis.

To study the population mean you need that the variable of interest has at least a normal distribution, there is no information about the distribution of the study variable but the sample size is large enough n≥30, so you can apply the central limit theorem to approximate the distribution of the sample mean to normal: X[bar]≈N(μ;σ²/n)

Thanks to this approximation it is valid to use an approximation of the standard normal distribution for the test:

$Z= \frac{X[bar]-Mu}{\frac{Sigma}{\sqrt{n} } }$ ≈N(0;1)

The critical values are:

$Z_{\alpha /2}= Z_{0.05}= -1.648$

$Z_{1-\alpha /2}= Z_{0.95}= 1.648$

You will reject the null hypothesis if $Z_{H_0}$ ≤-1.648 or if $Z_{H_0}$ ≥1.648

You will not reject the null hypothesis if -1.648< $Z_{H_0}$ <1.648

c)

$Z_{H_0}= \frac{X[bar]-Mu}{\frac{S}{\sqrt{n} } }= \frac{5.0611-5}{\frac{0.2803}{\sqrt{42} } }= 1.41$

d) The value of the statistic is between the two critical values so the decision is to not reject the null hypothesis. Then using a significance level of 10% there is no significant evidence to reject the null hypothesis so the valve plates have on average tensile strength of 5 lbs/mm.

e) The p-value is defined as the probability corresponding to the calculated statistic if possible under the null hypothesis (i.e. the probability of obtaining a value as extreme as the value of the statistic under the null hypothesis). If the test is two-tailed, so is the p-value, you can calculate it as:

P(Z≤-1.41) + P(Z≥1.41)= P(Z≤-1.41) + (1 - P(Z≤1.41))= 0.079 + ( 1 - 0.921)= 0.158

p-value: 0.158

I hope it helps!

5 0

3 years ago

MZLON is a straight angle.<br> mZLOM = 40 + 30°<br> mZMON = 83 + 90°<br> Find mZMON:

BlackZzzverrR [31]

The answer is 173 because 83+90 is 173

5 0

3 years ago