Joe is 6 feet tall and cast a 3 foot shadow. He is standing next to a building that cast a shadow that is 20 feet long. How tall
2 answers:
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Answer:
We can use the z score formula given by:
If we use this formula we got:
And using a calculator, excel or the normal standard table and we have that:
Step-by-step explanation:
We assume this previous info: It is known that the amounts of time required for room-service delivery at a certain Marriott Hotel are Normally distributed with the average delivery time of 20 minutes.
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 delivery times of a population, and for this case we know the distribution for X is given by:
Where and
Since the distribution for X is normal then the distribution for the sample mean is given by:
And we can use the z score formula given by:
If we use this formula we got:
And using a calculator, excel or the normal standard table and we have that:
Complete Question
A scientist believes the concentration of radon gas in the air is greater that the established safe level of 4 pci or less. The scientist tests the composition for 36 days finding an average concentration of 4.4 pci with a sample standard deviation of 1 pci.
a) In testing the scientist's belief, write the appropriate hypotheses:
Ha:
b) What decision should be made?
Answer:
a
The null hypothesis is
The alternative hypothesis is
b
There is sufficient evidence to conclude that the concentration of radon gas in the air is greater that the established safe level of 4pci or less
Step-by-step explanation:
From the question we are told that
The population mean is
The sample size
The sample mean is
The standard deviation is
The level of significance is
The null hypothesis is
The alternative hypothesis is
Generally the test statistics is mathematically represented as
=>
=>
=>
The p-value is mathematically represented as
From the z-table
So from this obtained value we see that
so we reject the null hypothesis
Hence we can conclude that there is sufficient evidence to conclude that the concentration of radon gas in the air is greater that the established safe level of 4pci or less