Problem
Due in 13 hours, 26 minutes. Due Wed 10/25/2023 10:00 am Keke's Kookies (htips:/Kekekookies.com/ 5 ) sells mini cookies in packs of 5 and has determined a probability distribution for the number of cookies that they sell in a given day. Make sure to round to 4 decimal places. \begin{tabular}{|c|c|c|c|c|c|} \hline $\mathrm{X}=$ Hsold & 0 & 5 & 10 & 15 & 20 \\ \hline Probability & 0.22 & 0.38 & 0.14 & $?$ & 0.07 \\ \hline \end{tabular} a. What is the probability of selling 15 mini cookies in a given day? b. Find the expected number of mini cookies sold in a day using the discrete probability distribution. c. Find the variance of the number of mini cookies sold in a day using the discrete probability distribution. d. Find the standard deviation of the number of mint cookies sold in a day using the discrete probability distribution. Points possible: 4 This is attempt 1 of 4 .
Solution
Step 1 ：Given the probabilities of selling 0, 5, 10, and 20 mini cookies in a day are 0.22, 0.38, 0.14, and 0.07 respectively.
Step 2 ：We know that the total probability should be 1. So we can calculate the missing probability by subtracting the sum of the given probabilities from 1.
Step 3 ：Let's denote the probability of selling 15 mini cookies in a day as \(P_{15}\).
Step 4 ：So, \(P_{15} = 1 - (0.22 + 0.38 + 0.14 + 0.07)\).
Step 5 ：Calculate the value of \(P_{15}\).
Step 6 ：\(P_{15} = 0.19\).
Step 7 ：Final Answer: The probability of selling 15 mini cookies in a given day is \(\boxed{0.19}\).
