Nathan is going to a water park today. He knows that the cost of admission is at least $12 per person. If c stands for the cost
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Answer:
And if we solve for a we got
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 hourly rates of a population, and for this case we know the distribution for X is given by:
For this part we want to find a value a, such that we satisfy this condition:
(a)
(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 0.80 of the area on the left and 0.20 of the area on the right it's z=0.842. On this case P(Z<0.842)=0.8 and P(z>0.842)=0.20
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
Answer:
a) 217
b) 1351
c) 5403
Step-by-step explanation:
Given that:
confidence interval (c) = 0.95
The Z score of is from the z table is given as:
Range = $45000 - $30000 = $15000
The standard deviation (σ) is given as:
Sample size (n) is given as:
a) E = $500
≈ 217
b) ≈ 1351
c) ≈ 5403