Question

the probability distribution of the number of people entering a store each day based on past data is given below. find the expected number of people for one day. round to the nearest tenth.

n people	76	84	98	89

Explanation:

Step1: Recall the formula for expected value

The expected value \( E(X) \) of a discrete random variable is calculated as \( E(X)=\sum_{i} x_i \cdot P(x_i) \), where \( x_i \) are the possible values and \( P(x_i) \) are their corresponding probabilities.

Step2: Calculate each term \( x_i \cdot P(x_i) \)

• For \( x_1 = 76 \) and \( P(x_1)=0.3 \): \( 76\times0.3 = 22.8 \)
• For \( x_2 = 84 \) and \( P(x_2)=0.2 \): \( 84\times0.2 = 16.8 \)
• For \( x_3 = 98 \) and \( P(x_3)=0.1 \): \( 98\times0.1 = 9.8 \)
• For \( x_4 = 89 \) and \( P(x_4)=0.4 \): \( 89\times0.4 = 35.6 \)

Step3: Sum the terms

Add up all the calculated terms: \( 22.8 + 16.8 + 9.8 + 35.6 \)
First, \( 22.8+16.8 = 39.6 \)
Then, \( 39.6+9.8 = 49.4 \)
Finally, \( 49.4+35.6 = 85.0 \)

Answer:

85.0