Question

The amounts a soft drink machine is designed to dispense for each drink are normally​ distributed, with a mean of 11.711.7 fluid ounces and a standard deviation of 0.30.3 fluid ounce. A drink is randomly selected. ​(a) Find the probability that the drink is less than 11.511.5 fluid ounces. ​(b) Find the probability that the drink is between 11.311.3 and 11.511.5 fluid ounces. ​(c) Find the probability that the drink is more than 12.312.3 fluid ounces. Can this be considered an unusual​ event? Explain your reasoning. ​(a) The probability that the drink is less than 11.511.5 fluid ounces is nothing. ​(Round to four decimal places as​ needed.) ​(b) The probability that the drink is between 11.311.3 and 11.511.5 fluid ounces is nothing. ​(Round to four decimal places as​ needed.) ​(c) The probability that the drink is more than 12.312.3 fluid ounces is nothing. ​(Round to four decimal places as​ needed.) Is a drink containing more than 12.312.3 fluid ounces an unusual​ event? Choose the correct answer below. A. NoNo​, because the probability that a drink contains more than 12.312.3 fluid ounces is greater thangreater than ​0.05, this event is notis not unusual. B. NoNo​, because the probability that a drink contains more than 12.312.3 fluid ounces is less thanless than ​0.05, this event is notis not unusual. C. YesYes​, because the probability that a drink contains more than 12.312.3 fluid ounces is less thanless than ​0.05, this event isis unusual. D. YesYes​, because the probability that a drink contains more than 12.312.3 fluid ounces is greater thangreater than ​0.05, this event isis unusual.

Answer 1

Solution,

Given that ,

mean = = 11.7

standard deviation = = 0.3

a) P(x < 11.5 ) = P[(x - ) / < ( 11.5 - 11.7) / 0.3 ]

= P(z < -0.67 )

Using z table,

= 0.2514

b) P(11.3 < x < 11.5 ) = P[( 11.3 - 11.7)/ 0.3 ) < (x - ) /  < ( 11.5 - 11.7) / 0.3 ) ]

= P( -1.33 < z < -0.67 )

= P(z < -0.67) - P(z < -1.33 )

Using z table

= 0.2514 - 0.0918

= 0.1596

c) P(x > 12.3 ) = 1 - P(x < 12.3)

= 1 - P[(x - ) / < ( 12.3 - 11.7) / 0.3]

= 1 - P(z < 2.00 )

Using z table

= 1 - 0.9772

= 0.0228

correct option is = C.

Yes, because the probability that a drinks contains more than 12.3 fluid ounces is less than 0.05,this event is unusual.