On Saturday Tami petaled to the state park at 21 mi/hr. After lunch she rode back at 14 mi/hr. if her total riding time was 5 ho
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Answer:
11.51% probability that the sample average will be less than 182
Step-by-step explanation:
To solve this question, we have 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 random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
What is the probability that the sample average will be less than 182
This is the pvalue of Z when X = 182. So
By the Central Limit Theorem
has a pvalue of 0.1151
11.51% probability that the sample average will be less than 182
We have been given that a rectangular auditorium seats 1702 people. Also, the number of seats in each row exceeds the number of rows by 9.
Let us assume that there are x rows in the auditorium. Therefore, there must be (x+9) seats in the each row. This will also be equal to the number of columns in the auditorium.
Therefore, we can set up an equation as:
We can now factor this quadratic as shown below:
Upon solving this equation, we get:
Since number of rows cannot be negative. Therefore, there must be 37 rows in the auditorium. And hence, the number of seats in each row will be 37+9=46 seats.