Calling Joe 45 minutes to the airport he arrived 90 minutes before his flight departed and then he spent 17 minutes in the air o

nce he landed Collins been 20 minutes Gathering his luggage and then he drove 35 minutes is Hotel what must be the true of any expression that represents the total time that Colin Spence traveling from his house to the hotel

Mathematics

1 answer:

USPshnik [31]3 years ago

3 0

$90 - 45 = 45 \\ 45 - 17 - 20 - 35$

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The lifetime of a certain type of battery is normally distributed with mean value 10 hours and standard deviation 1 hour. There

Oksi-84 [34.3K]

Answer:

$z=1.64$

And if we solve for a we got;

$10 +1.64*1=11.64$

So the value of height that separates the bottom 95% of data from the top 5% is 11.64

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 certain lifetime of a population, and for this case we know the distribution for X is given by:

$X \sim N(10,1)$

Where $\mu=10$ and $\sigma=1$

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.05$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.95 of the area on the left and 0.05 of the area on the right it's z=1.64. On this case P(Z<1.64)=0.95 and P(z>1.64)=0.05

If we use condition (b) from previous we have this:

$P(X$