This Question: 12 pts 16 of 31 (15 complete) The amounts a soft drink machine is

Question

This Question: 12 pts 16 of 31 (15 complete) The amounts a soft drink machine is designed to dispense for each drink are normally distributed, with a mean of 11.7 fluid ounces and a standard deviation of 0.2 fluid ounce. A drink is randomly selected (a) Find the probability that the drink is less than 11.6 fuid ounces (b) Find the probability that the drink is between 11.4 and 11.6 fluid ounces (c) Find the probability that the drink is more than 12.1 fluid ounces. Can this be considered an unusual event? Explain your reasoning (a) The probability that the dnnk is less than 11 6 fluid ounces is Round to four decimal places as needed.) (b) The probability that the drink is between 11.4 and 11.6 fluid ounces is Round to four decimal places as needed.) (c) The probability that the drink is more than 12.1 luid ounces is Round to four decimal places as needed.) Is a drink containing more than 12.1 fluid ounces an unusual event? Choose the correct answer bel O A. Yes, because the probability that a drink contains more than 12 1 audu unces is ess naris, this ,enn, unusual B. No, because the probability that a drink contains more than 12.1 fluid ouncesis less than 0.05, this event is not unusual. Il C. No, because the probability that a drink contains more than 12 1 fluid ounces is greater than 0 05. this event is not unusual. O D. Yes, because the probability that a drink contains more than 12.1 fluid ounces is greater than 0.05, this event is unusual Click to select your answer(s) evarcriptdoExereisel4);

Explanation / Answer

Mean = 11.7 fluid ounce

Standard deviation = 0.2 fluid ounce

P(X < A) = P(Z < (A - mean)/standard deviation)

a) P(X < 11.6) = P(Z < (11.6 - 11.7)/0.2)

= P(Z < -0.5)

= 0.3085

b) P(11.4 < X < 11.6) = P(X < 11.6) - P(X < 11.4)

= 0.3085 - P(Z < (11.4 - 11.7)/0.5)

= 0.3085 - P(Z < -1.5)

= 0.3085 - 0.0668

= 0.2417

c) P(X > 12.1) = 1 - P(X < 12.1)

= 1 - P(Z < (12.1 - 11.7)/0.2)

= 1 - P(Z < 2)

= 1 - 0.9773

= 0.0227

A. Yes, because the probability that a drink contain more than 12.1 fluid ounce is less than 0.05, this event is unusual.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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