Chapter 10.6, Problem 36PPS

a)

To determine

To calculate: The total served dishes.

Answer to Problem 36PPS

  $2635$Dishes

Explanation of Solution

Given: Green curry: with lentils and rice $=285$ , total $=845$

Red curry: with lentils and rice $=156$ , with plain rice $=180$ , total $=506$

Yellow curry: with lentils and rice $=346$ , with Naan bread $=427$ , total $=1284$

Total with Naan bread $=853$

Concept Used: A two-way relative frequency table: This is used to express the frequencies of data from the survey.

Calculation: Total red curry $=506$ , with lentils and rice $=156$ , with plain rice $=180$ ,

Number of red dishes with Naan bread $=506-156-180=170$

With lentils and rice green curry dishes $=285$ , red curry dishes $=156$ , and Yellow curry dishes $=346$ , Total $=285+156+346=787$

From total column: green curry dishes $=845$ , red curry $=506$ , and yellow curry $=1284$

Total $=845+506+1284=2635$

From total row: Total dishes $=2635$ , with lentils and rice $=787$ , with Naan bread $=853$

Total dishes with plain rice $=2635-787-853=995$

Dishes with Naan bread: red curry $=170$ , Yellow curry $=427$ , Total with Naan bread $=853$

Green dishes with Naan bread $=853-170-427=256$

Green curry dishes $=845$ , with lentils and rice green curry dishes $=285$ ,

With naan bread $=256$ , so, green dishes with plain rice $=845-285-256=304$

Total dishes with plain rice $=995$ , green dishes with plain rice $=304$ , Red curry $=180$

Yellow curry with plain rice $=995-304-180=511$

Curry flavour	With Lentils and Rice	With Plain Rice	With naan Bread	Total
Green curry	285	304	256	845
Red curry	156	180	170	506
Yellow curry	346	511	427	1284
Total	787	995	853	2635

Total dishes served $=2635$

Conclusion: $2635$Dishes

b)

To determine

To find the conditional relative frequency of green curry with Naan bread compared to green dishes.

Answer to Problem 36PPS

  $30\%$

Explanation of Solution

Given: Green curry: with lentils and rice $=285$ , total $=845$

Red curry: with lentils and rice $=156$ , with plain rice $=180$ , total $=506$

Yellow curry: with lentils and rice $=346$ , with Naan bread $=427$ , total $=1284$

Total with Naan bread $=853$

Concept Used: Conditional relative frequency is dividing a row or column by total row or column.

Calculation: Green dishes with naan bread $=256$ , Total green dishes $=845$

Conditional relative frequency $=\frac{256}{845}\approx 30\%$

Conclusion:

c)

To determine

To find the relative frequency of red curry with lentils and rice

Answer to Problem 36PPS

  $6\%$

Explanation of Solution

Given: Green curry: with lentils and rice $=285$ , total $=845$

Red curry: with lentils and rice $=156$ , with plain rice $=180$ , total $=506$

Yellow curry: with lentils and rice $=346$ , with Naan bread $=427$ , total $=1284$

Total with Naan bread $=853$

Concept Used: Relative frequency is dividing a row or column by total.

Calculation: Red curry with lentils and rice $=156$ , Total $=2635$

Relative frequency $=\frac{156}{2635}\approx 6\%$

Conclusion: Relative frequency $6\%$

d)

To determine

To find the marginal frequency of dishes served with plain rice.

Answer to Problem 36PPS

  $38\%$

Explanation of Solution

Given: Green curry: with lentils and rice $=285$ , total $=845$

Red curry: with lentils and rice $=156$ , with plain rice $=180$ , total $=506$

Yellow curry: with lentils and rice $=346$ , with Naan bread $=427$ , total $=1284$

Total with Naan bread $=853$

Concept Use: Marginal frequency is the sum of joint relative frequency of a row or column by total.

Calculation: With plain rice $=995$ , Total $=2635$

Marginal frequency $=\frac{995}{2635}\approx 38\%$

Conclusion: Marginal frequency $38\%$

e)

To determine

To find the marginal frequency of dishes served with plain rice.

Answer to Problem 36PPS

  $30\%$

Explanation of Solution

Given: Green curry: with lentils and rice $=285$ , total $=845$

Red curry: with lentils and rice $=156$ , with plain rice $=180$ , total $=506$

Yellow curry: with lentils and rice $=346$ , with Naan bread $=427$ , total $=1284$

Total with Naan bread $=853$

Concept Use: Marginal frequency is the sum of joint relative frequency of a row or column by total.

Calculation: With lentils and rice $=787$ , Total $=2635$

Marginal frequency $=\frac{995}{2635}\approx 30\%$

Conclusion: Marginal frequency $30\%$

f)

To determine

To find the conditional relative frequency of yellow curry with plain rice compared to plain rice dishes.

Answer to Problem 36PPS

  $51\%$

Explanation of Solution

Given: Green curry: with lentils and rice $=285$ , total $=845$

Red curry: with lentils and rice $=156$ , with plain rice $=180$ , total $=506$

Yellow curry: with lentils and rice $=346$ , with Naan bread $=427$ , total $=1284$

Total with Naan bread $=853$

Concept Use: Conditional relative frequency is dividing a row or column by total row or column.

Calculation: Yellow curry with plain rice $=511$ , Total pain rice dishes $=995$

Conditional relative frequency $=\frac{511}{995}\approx 51\%$

Conclusion: Conditional relative frequency $51\%$