2. You have read 175 novels of the 350 in your home, but your sister has read 190, of which only 55 are novels you have read as well. How many have neither of you read?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![**Problem Statement:**
You have read 175 novels of the 350 in your home, but your sister has read 190, of which only 55 are novels you have read as well. How many have neither of you read?
**Solution Explanation:**
To solve this problem, consider the following:
1. **Total Novels:** 350
2. **Novels You Have Read:** 175
3. **Novels Your Sister Has Read:** 190
4. **Novels Both Have Read:** 55
Using these numbers, we apply the inclusion-exclusion principle to find out how many novels have been read by either you or your sister:
\[
\text{Total novels read by either of you} = (\text{Novels you have read}) + (\text{Novels your sister has read}) - (\text{Novels both have read})
\]
\[
= 175 + 190 - 55 = 310
\]
5. **Novels Neither Have Read:**
Subtract the total novels read by either of you from the total number of novels:
\[
\text{Novels neither of you have read} = 350 - 310 = 40
\]
Thus, the number of novels that neither of you have read is 40.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb83496cd-9baf-4218-91af-6a9eb71001cb%2F0ea176cd-d458-436b-a5dd-193ed8c89a3a%2Fbom6ta_processed.jpeg&w=3840&q=75)
Let us denote :
A= number of novels read by me
B= number of novels read by sister
Given that n(A)=175, n(B)=190, n(A and B)=55
Using the union formula:
This means 310 novels are read by either me or my sister.
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