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Vlad1618 [11]
3 years ago
14

The lifetime of a certain type of TV tube has a normal distribution with a mean of 61 and a standard deviation of 6 months. What

portion of the tubes lasts between 57 and 59 months?
Mathematics
1 answer:
Ad libitum [116K]3 years ago
6 0

Answer:

P(57

P(-0.67

P(-0.67

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the lifetime for a TV of a population, and for this case we know the distribution for X is given by:

X \sim N(61,6)  

Where \mu=61 and \sigma=6

We are interested on this probability

P(57

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(57

And we can find this probability like this:

P(-0.67

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.  

P(-0.67

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Find the slope of the given line, if it is defined.
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Step-by-step explanation:

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Histograms are useful when we have data which can be divided into several classes or groups. The histogram shows the trend of each class and the trend among the different classes. For example when we have about 50 different values ranging from 1 to 20, it will be a better approach to draw a histogram in this case by dividing the data into small ranges e.g 1 to 4, 5 to 9 and so on and counting the frequency for each class.

Dot plot is useful when we have a small number of individual values. In this case we can visualize how many times each individual value occurred in the data. This is useful when the number of values in the data is less.

In the given scenario, we have 12 values in total ranging from 1 to 5. So making a dot plot would be the best choice. A histogram would not be useful in this case.

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Step-by-step explanation:

Given

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