A family decides to rent a boat for the day. The boats rental rate is $500 for the first two hours and $50 for each additional h
2 answers:
Answer:
4 is the maximum number of additional half-hours for which the family can rent the boat.
Step-by-step explanation:
Let us represent with x the number of additional half hours the boat can be rented.
Then notice the cost of renting the boat is modeled with the following expression:
Since it is the sum of the $500 for the first two hours plus the cost of the additional half hours which is the product of the cost of a single half hour $50 times the number of additional half-hours.
The family budgeted $700 therefore to cover the bill, therefore we have the following inequality:
We solve it for x:
Therefore, the family can rent the boat for a maximum number of 4 additional half hours
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Answer:
25.14% probability of observing a mean greater than 21
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
What is the probability of observing a mean greater than 21?
This is 1 subtracted by the pvalue of Z when X = 21. So
By the Central Limit Theorem
has a pvalue of 0.7486
1 - 0.7486 = 0.2514
25.14% probability of observing a mean greater than 21