Question

Butter side down Refer to the preceding exercise. Maria decides to test this

probability and drops $10$ pieces of toast from a $2.5$-foot table. Only $4$of them land butter

side down. Maria wants to perform a simulation to estimate the probability that $4$or

fewer pieces of toast out of $10$would land butter side down if the researchers’ $0.81$

probability value is correct.

a. Describe how you would use a table of random digits to perform the simulation.

b. Perform $3$trials of the simulation using the random digits given. Copy the digits onto

your paper and mark directly on or above them so that someone can follow what you

did.

$29077$	$14863$	$61683$	$47052$	$62224$	$51025$
$95052$	$90908$	$73592$	$75186$	$87136$	$95761$
$27102$	$56027$	$55892$	$33063$	$41842$	$81868$

c. The dotplot displays the results of 50 simulated trials of dropping $10$pieces of toast.

Is there convincing evidence that the researchers’ $0.81$probability value is incorrect?

Explain your answer.

Short answer

(a)First we will select a row and then we will select a two - digit number,

if the number lies between $00$to $80$(both including),

then toast will land butter side down,otherwise

toast will land butter side up.

(b)First trial:$10$toast lie butter side down and $0$toast lie butter side up.

Second trial:$9$toast lie butter side down and $1$ toast lie butter side up.

Third trial: $8$toast lie butter side down and $2$ toast lie butter side up.

(c)No, there is no convincing evidence that the researchers’ $0.81$probability value is incorrect.

Step-by-step solution

Part (a) Step 1:Given Information

We have been given that,

Maria wants to perform a simulation , the probability that $4$or fewer pieces of toast out of $10$would land butter side down if the researchers’ probability value is correct =$0.81$

probability of toast landing butter side down =$0.81$

$29077$	$14863$	$61683$	$47052$	$62224$	$51025$
$95052$	$90908$	$73592$	$75186$	$87136$	$95761$
$27102$	$56027$	$55892$	$33063$	$41842$	$81868$

Part (a) Step 2:Explanation

First we will select a row and then we will select a two - digit number,

if the number lies between $00$to $80$(both including),

then toast will land butter side down,otherwise

toast will land butter side up.

Number of trials given to perform = $10$

So,we will select $10$numbers.

Record the number of toast that land butter side down out of $10$.

Part (b) Step 1:Given Information

We have been given that,

Maria wants to perform a simulation , the probability that $4$or fewer pieces of toast out of $4$would land butter side down. if the researchers’ probability value is correct =$0.81$

probability of toast landing butter side down =$0.81$

Part (b) Step 2:Explanation

First we will select a row and then we will select a two - digit number,

if the number lies between $00$to $80$(both including),

then toast will land butter side down,otherwise

toast will land butter side up.

We have selected first row and the first two-digit number selected is $29$.

First trial:

numbers selected are,

$29,07,71,48,63,61,68,34,70,52$

all the selected numbers are between $00$to $80$.

So,$10$toast lie butter side down and $0$toast lie butter side up.

Second trial:

numbers selected are,

$62,22,45,10,25,95,05,29,09,08$

all the selected numbers are between $00$to $80$except $95$.

So, $9$toast lie butter side down and $1$toast lie butter side up.

Third trial:

numbers selected are,

$73,59,27,51,86,87,13,69,57,61$

all the selected numbers are between $00$to $80$except $86,87$.

So, $8$ toast lie butter side down and $2$ toast lie butter side up.

Part (c) Step 1:Given Information

We have been given that,

Maria wants to perform a simulation , the probability that $4$or fewer pieces of toast out of $4$would land butter side down. if the researchers’ probability value is correct =$0.81$

probability of toast landing butter side down =$0.81$

Part (c) Step 2:Explanation

Number of toast used for simulation=$10$

Probability of toast falling butter side down =$0.81$

Number of toast falling butter side down = $0.81*10$=$8.1$

approximately,$8$toast fall butter side down.

In the given dotplot of $50$simulated trials of dropping $10$pieces of toast ,$8$consists of maximum number of dots.

So,there is no convincing evidence that the researchers’ $0.81$probability value is incorrect.