Question

Triton is a wholesale supplier of canola oil. Triton sells a mean of 8 thousand gallons per day with a standard deviation of 1.5 thousand gallons per day. Assuming that demand is normally distributed, what is the probability that demand per day, in thousands of gallons will be:

1. Between 9.5 thousand gallons and 10.0 thousand gallons?

2. Less than 5 thousand gallons?

3. What volume represents the largest 10%?

Answer 1

GIVEN:

Let is a normally distributed variable which represents the demand per day.

Mean supply of canola oil thousand gallons per day

Standard deviation thousand gallons per day

SOLUTION:

To calculate the probability, we convert the raw score (x) into standard score (z) by using the formula,

1) PROBABILITY THAT DEMAND PER DAY IS BETWEEN 9.5 AND 10.0 THOUSAND GALLONS:

The probability that demand per day between 9.5 and 10.0 thousand gallons is,

  

{Since }

Using the z table, the first probability value is the value with corresponding row 1.3 and column 0.03 and the second probability value is the value with corresponding row 1.0 and column 0.00.

The probability that demand per day between 9.5 and 10.0 thousand gallons is .

2) PROBABILITY THAT DEMAND PER DAY IS LESS THAN 5 THOUSAND GALLONS:

The probability that demand per day less than 5 thousand gallons is,

  

Using the z table, the probability value is the value with corresponding row -2.0 and column 0.00.

The probability that demand per day less than 5 thousand gallons is .

3) WHAT VOLUME REPRESENTS THE LARGEST 10%:

The problem is to find value from the probability. We want to find the value that has 10% of the volume to the right of it.

Given the area to the left:

Now the z score corresponding to the probability value 0.9000 is with 1.2 row and 0.08 column.

Now using the formula,

Thus the canola oil volume of 9.92 thousand gallons represents the largest 10%.