Question

a machine at the candy factory dispensed different numbers of lemon - flavored candies into various bags.
lemon - flavored candies per bag
150 175 150 143 50 175 150 150 143 143 143 143 150 50
143 175 50 150 150 143
x is the number of lemon - flavored candies that a randomly chosen bag had. what is the expected value of x?
write your answer as a decimal.

Explanation:

Step1: Count the frequency of each value

50 appears 3 times, 143 appears 8 times, 150 appears 9 times, 175 appears 3 times. Total number of data - points is $3 + 8+9 + 3=23$.

Step2: Calculate the probability of each value

$P(50)=\frac{3}{23}$, $P(143)=\frac{8}{23}$, $P(150)=\frac{9}{23}$, $P(175)=\frac{3}{23}$.

Step3: Use the expected - value formula $E(X)=\sum_{i}x_{i}P(x_{i})$

$E(X)=50\times\frac{3}{23}+143\times\frac{8}{23}+150\times\frac{9}{23}+175\times\frac{3}{23}$
$=\frac{150 + 1144+1350 + 525}{23}$
$=\frac{3169}{23}\approx137.78$

Answer:

$137.78$