Question

kelsie works at a bicycle shop as a salesperson. she records the number of bicycles she sells on a daily basis. here is the probability distribution of ( b = ) the number of bicycles kelsie sells on a randomly selected day, and ( t = ) the time she spends filling out daily sales reports.

( b = # ) of bicycles sold ( 0 ) ( 1 ) ( 2 ) ( 3 ) ( t = ) time (minutes) ( 10 ) ( 20 ) ( 30 ) ( 40 ) probability ( 0.30 ) ( 0.50 ) ( 0.15 ) ( 0.05 )

calculate the mean of ( b ).

( mu_b=) bicycles

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Explanation:

Step1: Recall the formula for the mean of a discrete random variable

The mean formula is $\mu=\sum x\cdot P(x)$.

Step2: Calculate each term

For $x = 0$: $0\times0.30 = 0$.
For $x = 1$: $1\times0.50 = 0.5$.
For $x = 2$: $2\times0.15 = 0.3$.
For $x = 3$: $3\times0.05 = 0.15$.

Step3: Sum up the terms

$\mu_B=0 + 0.5+0.3 + 0.15$.

Answer:

$0.95$ bicycles