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Suppose that the supplier states that the price might be as low as [tex]$105 or as high as $[/tex]165 per unit. Without any other information, a uniform distribution is a reasonable model.

What is the price if RAND() generates the random number 0.55?

Sagot :

To determine the price based on a uniform distribution, we need to follow these steps:

1. Identify the minimum and maximum values given by the supplier.
- The minimum price (low price) is [tex]$105. - The maximum price (high price) is $[/tex]165.

2. Utilize the random number generated by the `RAND()` function, which in this case is 0.55.

3. Calculate the price using the formula for a uniform distribution. The formula is:
[tex]\[ \text{Price} = \text{Low Price} + (\text{High Price} - \text{Low Price}) \times \text{Random Number} \][/tex]

4. Substitute the values into the formula:
[tex]\[ \text{Price} = 105 + (165 - 105) \times 0.55 \][/tex]

5. Simplify the expression within the parentheses first:
[tex]\[ 165 - 105 = 60 \][/tex]

6. Multiply the result by the random number:
[tex]\[ 60 \times 0.55 = 33 \][/tex]

7. Finally, add this value to the low price:
[tex]\[ 105 + 33 = 138 \][/tex]

Therefore, if RAND() generates the random number 0.55, the price would be $138.