Question

The amount of distilled water dispensed by a certain machine has a normal distribution with μ=64ozandσ=0.78oz. When you put you water bottle in to fill it up:

a. What is the probability that the amount of water dispensed is between 62 and 63 oz?

b. What is the probability that the amount of water dispensed is greater than 65 oz?

c. What container size will ensure that overflow occurs only 5% of the time?

Answer 1

Answer Date: 18/05/2019 a) The probability thatthe amount ofwater dispensed is between 62 and 63 oz is, First, compute thez score then find probability based on standard normal table. For x = 62 converts to 62- 64 0.78 --2.56 For x = 63 converts to 63- 64 0.78 -1 .28

From the standard normal distribution table, the associated probability for z values and subtracts the probability is, p(62 s r s 63)-p(-2.56 3 z s-1.28) -p(z-1.28) p(Z s -2.56) 0.1003 0.0052 0.0951 The probability that the amount ofwater dispensed is between 62 and 63 oz is 0.0951 b) The probability is that the amount of water dispensed is greater than 65 oz is First, compute thez score then find probability based on standard normal table.

For x 65 converts to 65 -64 0.78 From the standard normal distribution table, the associated probability is 0.8997. Since find the area to the right, so subtract from 1 to get, 1-0.8997 0.1003 The probability is that the amount of water dispensed is greater than 65 oz is 0.1003 c) The container size is.

From the standard normal table, the indicated z score for the area of 0.05000 subtract from 1 and indicative area 0.9500 is 1.645 -64 + (1.645x 0 .78) - 65.28 The container size is 65.28