Answer :
Having the probability distribution in the range from 0 to 20, the sum of all probabilities should give 1. This will be useful to estimate the missing value (P(x = 15)).
Let's establish the sum of probabilities:
[tex]P(x=0)+P(x=5)+P(x=10)+P(x=15)+P(x=20)=1[/tex]Now, we can replace values and solve for P(x = 15):
[tex]0.11+0.3+0.21+P(x=15)+0.1=1[/tex][tex]0.72+P(x=15)=1[/tex][tex]\begin{gathered} P(x=15)=1-0.72 \\ P(x=15)=0.28 \end{gathered}[/tex]The probability of selling 15 cheesecakes on a given day is 0.28 (28%)
Now, to estimate the probability of selling at least 10 cheesecakes can be calculated by summing the probabilities of selling 10, 15, or 20. In this case, we include the 10 because it says at least. Then:
[tex]P(x\ge10)=P(x=10)+P(x=15)+P(x=20)[/tex]Replacing values:
[tex]P(x\ge10)=0.21+0.28+0.1[/tex][tex]P(x\ge10)=0.59[/tex]The probability of selling at least 10 is 0.59 (59%))
