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Median is the middle value, if you have an even number of values in the data set, add the two middle numbers and divide that by two. If you have an odd number in the data set, it would be the middle number.
Upper quartile is the middle value of the upper half of numbers in the data set, The upper half of numbers are the numbers below the Median. Use same way as the median to find the value.
Minimum is the lowest number in the set.
Maximum is the highest number in the set.
Lower quartile is the middle value of the lower half of numbers in the data set, The lower half of numbers are the numbers above the Median. Use same way as the median to find the value.
See the attached picture:
Upper quartile is the middle value of the upper half of numbers in the data set, The upper half of numbers are the numbers below the Median. Use same way as the median to find the value.
Minimum is the lowest number in the set.
Maximum is the highest number in the set.
Lower quartile is the middle value of the lower half of numbers in the data set, The lower half of numbers are the numbers above the Median. Use same way as the median to find the value.
See the attached picture:
Answer:
0.73% probability that their mean length is less than 11.1 inches
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, which is also called standard error
In this problem, we have that:
What is the probability that their mean length is less than 11.1 inches
This is the pvalue of Z when X = 11.1. So
By the Central Limit Theorem
has a pvalue of 0.0073.
0.73% probability that their mean length is less than 11.1 inches