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Greenfields is a mail order seed and plant business. The size of orders is uniformly distributed over the interval from $25 to $80. Use the following random numbers to generate the size of 10 orders. .41 .99 .07 .05 .38 .77 .19 .12 .58 .60 What is the value for the first order size generated randomly based on random number 0.41? What is the value for the last order size generated randomly based on random number 0.60? What is the average order size?

Sagot :

batolisis

Answer:

a) 47.55

b) 58

c) 47.88

Step-by-step explanation:

Given that the size of the orders is uniformly distributed over the interval

$25 ( a ) to $80 ( b )

a) Determine the value for the first order size generated based on 0.41

parameter for normal distribution is given as ;  a = 25,  b = 80

size/value of order  = a + random number ( b - a )

                                = 25 + 0.41 ( 80 - 25 )

                                =  47.55

b) Value of the last order generated based on random number (0.6)

= a + random number ( b - a )

= 25 + 0.6 ( 80 - 25 )

= 25 + 33 = 58

c) Average order size

= ∑ order 1 + order 2 + ----- + order 10  ) / 10

= (47.55 + ...... + 58 ) / 10

= 478.8 / 10 = 47.88

MrRoyal

The mail order seed follows a uniform distribution

(a) The value of the first order size generated by 0.41

The given parameters are:

[tex]a = 25[/tex] -- the lower bound

[tex]b = 80[/tex] -- the upper bound

To calculate the required value, we make use of the following order formula

[tex]Value = a + r(b - a)[/tex]

Where r represents the random number.

So, we have:

[tex]Value= 25 + 0.41 \times ( 80 - 25 )[/tex]

Open bracket

[tex]Value= 25 + 0.41 \times 55[/tex]

Evaluate the product

[tex]Value= 25 + 22.55[/tex]

Add the terms

[tex]Value= 47.55[/tex]

Hence,  the value for the first order size generated randomly based on random number 0.41 is 47.55

(b) The value of the last order size generated by 0.60

In (a), we have:

[tex]Value = a + r(b - a)[/tex]

So, we have:

[tex]Value= 25 + 0.60 \times ( 80 - 25 )[/tex]

Open bracket

[tex]Value= 25 + 0.60 \times 55[/tex]

Evaluate the product

[tex]Value= 25 + 33[/tex]

Add the terms

[tex]Value= 58[/tex]

Hence, the value for the last order size generated randomly based on random number 0.61 is 58

(c) The average order size

To do this, we calculate the order size from 1 to 10, and then calculate the average value of the 10 orders.

Using a calculator, the sum of the 10 orders is:

[tex]\sum x= 478.8[/tex]

The average order size is then calculated as:

[tex]\bar x = \frac{\sum x}{n}[/tex]

This gives

[tex]\sum x= \frac{478.8}{10}[/tex]

[tex]\sum x= 47.88[/tex]

Hence, the average order size is 47.88

Read more about uniform distribution at:

https://brainly.com/question/25195809

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