Is my work correct here I'm supposed to find the first four terms using the recursion formula?

The mean life of a television set is 119119 months with a standard deviation of 1414 months. If a sample of 7474 televisions is

Pepsi [2]

Answer:

0.5034 = 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 can be 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

In this problem, we have that:

$\mu = 119, \sigma = 14, n = 74, s = \frac{14}{\sqrt{74}} = 1.6275$

What is the probability that the sample mean would differ from the true mean by less than 1.11 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

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

$Z = \frac{120.1 - 119}{1.6275}$

$Z = 0.68$

$Z = 0.68$ has a pvalue of 0.7517

X = 117.9

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

$Z = \frac{117.9 - 119}{1.6275}$

$Z = -0.68$

$Z = -0.68$ has a pvalue of 0.2483

0.7517 - 0.2483 = 0.5034

0.5034 = 50.34% probability that the sample mean would differ from the true mean by less than 1.1 months

3 0

3 years ago

The scale from a playground to a scale drawing of the playground is 4 meters per centimeter.The length of the drawing of the pla

Scilla [17]

Answer:

322.24 meters

Step-by-step explanation:

The scale is 4 meter per centimeter. Multiply 5.3 by 4 to get 21.2 meters. Multiply 5.3 by 4 to get 15.2 meters. Multiply 21.2 by 15.2 to get 322.24

6 0

2 years ago

In a study relating the degree of warping, in mm, of a copper plate (y) to temperature in °C (x), the following summary statisti

kipiarov [429]

Answer:

The error sum of squares is SSE=12.97

The regression sum of squares is SSR=6.430

The total sum of squares is SST=19.4

Step-by-step explanation:

Linear regression is a way "to modeling the relationship between a scalar response (or dependent variable) and one or more explanatory variables (or independent variables)".

Regression estimates are "used to describe data and to explain the relationship between one dependent variable and one or more independent variables"

The linear model is given by the following equation $Y=mx +b$ , where y is the dependent variable, x the independent variable, m the slope and b the intercept.

For this case we have the following info given:

$\sum_{i=1}^n (x_i -\bar x)^2 =98775$

$\sum_{i=1}^n (y_i -\bar y)^2 =19.4$

$\bar x =26.36$

$\bar y =0.5188$

n= 40 represent the sample size

$\sum_{i=1}^n (x_i -\bar x)(y_i -\bar y) =796.94$

The total sum of squares is given by this formula:

$SST= \sum_{i=1}^n (y_i -\bar y)^2 =19.4$

And from the formulas for a simple regression, we need to calculate the slope for the regression like this:

$m=\frac{\sum_{i=1}^n (x_i -\bar x)(y_i -\bar y)}{\sum_{i=1}^n (x_i -\bar x)^2}$

And if we replace the values given we have:

$m=\frac{796.94}{98775}=0.008068$

We have another useful equation in order to find the sum of squares for the regression, given by:

$SSR=m* \sum_{i=1}^n (x_i -\bar x)(y_i -\bar y)=0.008068*796.94=6.430$

And we know this equivalence:

$SST= SSR+SSE$

And solving for the sum of squares for the error we have:

$SSE=SST-SSR=19.4-6.430=12.97$

So then we have the final solutions:

The error sum of squares is SSE=12.97

The regression sum of squares is SSR=6.430

The total sum of squares is SST=19.4

6 0

3 years ago

What is the pattern of the trend line equation in this graph?

kondaur [170]

The pattern of the trend line from what we can see here shows the existence of a positive upward trend.

<h3>What is a positive upward trend?</h3>

We can see that the graph has fluctuations which have an upward trend over the years. This upward trend can be gotten from the straight line that was drawn on the graph.

It slants to the top. This shows us that the trend is positive and rising over the period of time that we have in the graph. In the graph, the upward trend can be seen from the fact that there has been a rise in the temperature of the city over the time period that was illustrated. The increase in temperature rose from 31.5 to 33 degrees period of time.

Hence we can conclude that The pattern of the trend line from what we can see here shows the existence of a positive upward trend.

Read more on trend lines here: brainly.com/question/27194207

#SPJ1

4 0

1 year ago

What is the final concentration if a saline solution consisting of 20% NaCl is diluted using a 1/4 solution?

vodomira [7]

Answer: C.V=C1.V1 +C2.V2

Step-by-step explanation: C=(C1V1 + C2V2)/V -> C=(20%.V+25%V)/2V-> C=22,5%

6 0

3 years ago