Questions: You are given two tables below. The data from the frequency distribution table was used to calculate the values in the probability distribution table. Find the missing values of x and y in the table: Frequency Distribution Table Number of fish caught 0 1 2 3 4 Frequency 88 72 30 8 2 Probability Distribution Table Number of fish caught 0 1 2 3 4 Probability 0.44 x 0.15 y 0.01 x= y=

You are given two tables below. The data from the frequency distribution table was used to calculate the values in the probability distribution table. Find the missing values of x and y in the table:

Frequency Distribution Table
Number of fish caught 0 1 2 3 4
Frequency 88 72 30 8 2

Probability Distribution Table
Number of fish caught 0 1 2 3 4
Probability 0.44 x 0.15 y 0.01

x=
y=

Transcript text: You are given two tables below. The data from the frequency distribution table was used to calculate the values in the probability distribution table. Find the missing values of $x$ and $y$ in the table: Frequency Distribution Table \begin{tabular}{|l|c|c|c|c|c|} \hline Number of fish caught & 0 & 1 & 2 & 3 & 4 \\ \hline Frequency & 88 & 72 & 30 & 8 & 2 \\ \hline \end{tabular} Probability Distribution Table \begin{tabular}{|l|c|c|c|c|c|} \hline Number of fish caught & 0 & 1 & 2 & 3 & 4 \\ \hline Probability & 0.44 & $x$ & 0.15 & $y$ & 0.01 \\ \hline \end{tabular} \[ \begin{array}{l} x=\square \\ y=\square \end{array} \]

Solution

Solution Steps

To find the missing values $ x $ and $ y $ in the probability distribution table, we first need to calculate the total number of observations from the frequency distribution table. Then, we can determine the probabilities by dividing each frequency by the total number of observations. The missing probabilities $ x $ and $ y $ can be calculated using this method.

Step 1: Calculate Total Observations

To find the total number of observations, sum the frequencies from the frequency distribution table: \[ \text{Total Observations} = 88 + 72 + 30 + 8 + 2 = 200 \]

Step 2: Calculate Probabilities

The probability for each number of fish caught is calculated by dividing the frequency by the total number of observations. The probabilities are: \[ \begin{align_} P(0) &= \frac{88}{200} = 0.44, \\ P(1) &= \frac{72}{200} = 0.36, \\ P(2) &= \frac{30}{200} = 0.15, \\ P(3) &= \frac{8}{200} = 0.04, \\ P(4) &= \frac{2}{200} = 0.01. \end{align_} \]

Step 3: Identify Missing Values

From the probability distribution table, the missing values $ x $ and $ y $ correspond to the probabilities for catching 1 and 3 fish, respectively: \[ \begin{align_} x &= P(1) = 0.36, \\ y &= P(3) = 0.04. \end{align_} \]