The height of a triangle is 4 in. greater than twice its base. The area of the triangle is no more than 168 in.2. Which inequali
2 answers:
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Answer:
a) By the Central Limit Theorem, the distribution would be approximately normal, with mean and standard deviation
b) 4.02 standard deviations below the mean.
c) Making 25 or less shots has a pvalue of -4.02. Z-scores lower than -2 are considered surprising, so yes, it would be surprising for him to make only 25 of these shots.
Step-by-step explanation:
To solve this question, we are going to 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.
For proportions, we have that the mean is and the standard deviation is
In this problem, we have that:
a)By the Central Limit Theorem, the distribution would be approximately normal, with mean and standard deviation
b)This is Z when X = 0.25.
By the Central Limit Theorem
4.02 standard deviations below the mean.
c) Making 25 or less shots has a pvalue of -4.02. Z-scores lower than -2 are considered
surprising, so yes, it would be surprising for him to make only 25 of these shots.
The plot that organizes the data into 4 groups of equal sizes is box and whisker plot.
The image below shows a box and whisker plot. Following are the elements of box and whisker plot:
Minimum = This is the smallest value of the data set
Q1 = First (Lower) Quartile of the data set. 25% of the data values lie below this point
Q2 = Second Quartile or Median. This is the central value so 50% of the data values lie below this point
Q3 = Third (Upper) Quartile of the data set. 75% of the data values lie below this point.
Maximum = This is the maximum value of the data set.
Based on box and whisker plot we can compare two or more sets of data by comparing the spread of the data. We can also directly observe from the box and whisker plot if the data is uniform, normal or skewed. Using box and whisker plot we can also visualize any outliers that may be in the data.
