the probability distribution for the number of students in statistics classes offered at a college is given…

the probability distribution for the number of students in statistics classes offered at a college is given, but one value is missing. fill in the missing value, then find the expected value of the probability distribution. \n| x | p(x) |\n|----|----| \n| 24 | 0.08 |\n| 25 | 0.12 |\n| 26 | 0.15 |\n| 27 | |\n| 28 | 0.1 |\nround the answer to two decimal places. find the mean number of students in a statistics class at the college: students

the probability distribution for the number of students in statistics classes offered at a college is given, but one value is missing. fill in the missing value, then find the expected value of the probability distribution. \n| x | p(x) |\n|----|----| \n| 24 | 0.08 |\n| 25 | 0.12 |\n| 26 | 0.15 |\n| 27 | |\n| 28 | 0.1 |\nround the answer to two decimal places. find the mean number of students in a statistics class at the college: students

Answer

Explanation:

Step1: Find the missing probability

The sum of all probabilities in a probability - distribution is 1. Let the missing probability be $p$. Then $0.08 + 0.12+0.15 + p+0.1=1$. $p = 1-(0.08 + 0.12+0.15 + 0.1)=1 - 0.45=0.55$.

Step2: Calculate the expected value

The formula for the expected value $E(X)$ of a discrete probability distribution is $E(X)=\sum_{i}x_ip_i$. $E(X)=24\times0.08 + 25\times0.12+26\times0.15 + 27\times0.55+28\times0.1$ $E(X)=1.92+3 + 3.9+14.85 + 2.8$ $E(X)=26.47$.

Answer:

26.47