The amounts a soft drink machine is designed to dispense for each drink, are nor

Question

The amounts a soft drink machine is designed to dispense for each drink, are normally distributed with a mean 12.1 fluid ounces A drink is randomly (a) Find the probability that the drink is less than 11.9 fluid ounces (b) Find the probability that the drink is between 11.6 and 11.9 fluid ounces (c) Find the probability that the drink is more than 12.5 fluid ounces. Can this be unusual event? Explain your reasoning (a)The probability that the drink is less than 11.9 fluid ounces is 0.2514 (b) the probability that the drink is between 11.5 and 11.9 fluid ounces is 0.2039 (rounded to four decimal places as needed) (c) the probability that the drink is more than 12.5 fluid ounces is (rounded to four decimal places as needed) is a drink containing more than 12.5 fluid ounces an unusual

Explanation / Answer

(a)For X=11.9, z=(x-mu)/sigma=(11.9-12.1)/0.3=-0.67

P(X<11.9)=P(z<-0.67)=0.2514

(b)For X=11.6, z=(11.6-12.1)/0.3=-1.67

P(11.6<X<11.9)=P(X<11.9)-P(X<11.6)

=P(z<-0.67)-P(z<-1.67)

=0.2514-0.0475

=0.2039

(c)For X=12.5, z=(12.5-12.1)/0.3=1.33

P(X>12.5)=P(z>1.33)=1-P(z<1.33)=1-0.9082=0.0918

(d)In a drink containing more than 12.5 ounce is not unusual as the probability is not less than 0.05.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.