Answer: B
Step-by-step explanation:
Noah manages a buffet at a local restaurant. He charges $10 for the buffet. On average, 16 customers choose the buffet as their
meal every hour. After surveying several customers, Noah has determined that for every $1 increase in the cost of the buffet, the average number of customers who select the buffet will decrease by 2 per hour. The restaurant owner wants the buffet to maintain a minimum revenue of $130 per hour. Noah wants to model this situation with an inequality and use the model to help him make the best pricing decisions. Assuming that any increase occurs in whole dollar amounts, what is the maximum possible increase that maintains the desired minimum revenue? Explain why this is true.
1 answer:
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Answer:
(a)
(b) 0.7910
(c) 0.0401
(d) 0.6464
Step-by-step explanation:
Let <em>X</em> = amount of time that people spend at Grover Hot Springs.
The random variable <em>X</em> is normally distributed with a mean of 73 minutes and a standard deviation of 16 minutes.
(a)
The distribution of the random variable <em>X</em> is:
(b)
Compute the probability that a randomly selected person at the hot springs stays longer than 60 minutes as follows:
*Use a <em>z</em>-table for the probability.
Thus, the probability that a randomly selected person at the hot springs stays longer than an hour is 0.7910.
(c)
Compute the probability that a randomly selected person at the hot springs stays less than 45 minutes as follows:
*Use a <em>z</em>-table for the probability.
Thus, the probability that a randomly selected person at the hot springs stays less than 45 minutes is 0.0401.
(d)
Compute the probability that a randomly person spends between 60 and 90 minutes at the hot springs as follows:
*Use a <em>z</em>-table for the probability.
Thus, the probability that a randomly person spends between 60 and 90 minutes at the hot springs is 0.6464
Answer:
The 99% confidence interval would be given by (58.373;65.627)
We are 99% confident that the true mean for the variable of interest is between 58.373 and 65.627.
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
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".
represent the sample mean
population mean (variable of interest)
s=8 represent the sample standard deviation
n=36 represent the sample size
Part a: Confidence interval
The confidence interval for the mean is given by the following formula:
(1)
In order to calculate the critical value we need to find first the degrees of freedom, given by:
Since the Confidence is 0.99 or 99%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,35)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 99% confidence interval would be given by (58.373;65.627)
We are 99% confident that the true mean for the variable of interest is between 58.373 and 65.627.