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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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