Questions: Chapter 5.2 and 5.4-Discrete and A local bakery has determined a probability distribution for the number of cheesecakes that they sell in a given day. X= #sold 0 5 10 15 20 Probability 0.11 0.34 0.08 ...? 0.14 a. What is the probability of selling 15 cheesecakes in a given day? 0.33 b. What is the probability of selling at least 10 cheesecakes? 0.55 c. What is the probability of selling 5 or 15 cheesecakes? 0.67 d. What is the probability of selling 25 cheesecakes? e. Give the expected number of cheesecakes sold in a day using the discrete probability distribution? f. What is the probability of selling at most 10 cheesecakes? 0.53

Chapter 5.2 and 5.4-Discrete and

A local bakery has determined a probability distribution for the number of cheesecakes that they sell in a given day.
X= #sold 0 5 10 15 20
Probability 0.11 0.34 0.08 ...? 0.14

a. What is the probability of selling 15 cheesecakes in a given day? 0.33
b. What is the probability of selling at least 10 cheesecakes? 0.55
c. What is the probability of selling 5 or 15 cheesecakes? 0.67
d. What is the probability of selling 25 cheesecakes?
e. Give the expected number of cheesecakes sold in a day using the discrete probability distribution?
f. What is the probability of selling at most 10 cheesecakes? 0.53

Transcript text: Chapter 5.2 and 5.4-Discrete and A local bakery has determined a probability distribution for the number of cheesecakes that they sell in a given day. \begin{tabular}{|c|c|c|c|c|c|} \hline$X=$ \#sold & 0 & 5 & 10 & 15 & 20 \\ \hline Probability & 0.11 & 0.34 & 0.08 & $\ldots ?$ & 0.14 \\ \hline \end{tabular} a. What is the probability of selling 15 cheesecakes in a given day? 0.33 $\square$ of b. What is the probability of selling at least 10 cheesecakes? 0.55 $\square$ 0 c. What is the probability of selling 5 or 15 cheesecakes? $\square$ 0.67 $0^{\circ}$ d. What is the probability of selling 25 cheesecakes? $\square$ $\sigma^{6}$ e. Give the expected number of cheesecakes sold in a day using the discrete probability distribution? $\square$ f. What is the probability of selling at most 10 cheesecakes? $\square$ 0.53 $0^{6}$

Solution

Solution Steps

Step 1: Calculate the Probability of Selling 15 Cheesecakes

To find the probability of selling 15 cheesecakes, we calculated the missing probability in the distribution. The probability of selling 15 cheesecakes is given by:

\[ P(X = 15) = 0.33 \]

Step 2: Calculate the Probability of Selling at Least 10 Cheesecakes

The probability of selling at least 10 cheesecakes is the sum of the probabilities of selling 10, 15, and 20 cheesecakes:

\[ P(X \geq 10) = P(X = 10) + P(X = 15) + P(X = 20) = 0.08 + 0.33 + 0.14 = 0.55 \]

Step 3: Calculate the Probability of Selling 5 or 15 Cheesecakes

The probability of selling either 5 or 15 cheesecakes is the sum of their respective probabilities:

\[ P(X = 5 \text{ or } X = 15) = P(X = 5) + P(X = 15) = 0.34 + 0.33 = 0.67 \]