Question

Help with this bounds question please

Answer 1

Answer: 6.68km/litre

Explanation:

Distance(d) = 187km ( to 3 significant figures)

Petrol(p) = 28litres ( to 2 significant figures)

A number, x, rounded to 1 significant figure is 200

Write down the error interval for x

Calculating the lower and upper bound for both 'd' and 'p'

Upper bound 'd' = 187.5km

Lower bound 'd' = 186.5km

Upper bound 'p' = 28.5km

Lower bound 'p' = 27.5km

Therefore,

Petrol consumption (C) = d/p

Upper C = 187.5 / 28.5 = 6.57894

Lower C = 186.5 / 27.5 = 6.781818

Accuracy answer for C = (6.57894 + 6.781818) / 2 = 6.680379

= 6.68km/ litre ( to 3 significant figures)

To achieve a reasonable level of accuracy, the upper and lower bounds of P and D was used to calculate C, which was then averaged.

Using 3 significant figures ensure that we capture the C better, instead of early rounding.

Answer 2

By considering bounds, the value of c for David's journey to a suitable degree of accuracy is equal to 7 km per litre.

In Mathematics and Statistics, the margin of error (MOE) is a measure of the difference that exist between an observed value and an actual value of the population parameter.

Based on the information provided about the distance driven by David, we would determine the boundaries for the petrol consumption (c) of a car as follows;

187 km: 186.5 ≤ d < 187.5

28 litres: 27.5 ≤ p < 28.5

Lower boundary, c = d/p

Lower boundary = 186.5/28.5

Lower boundary = 6.54

Upper boundary = 187.5/27.5

Upper boundary = 6.82 km per litre.

Now, we can rewrite the boundaries for the petrol consumption (c) of a car as follows;

6.54 ≤ c < 6.82

By approximating to a suitable degree of accuracy, the value of c is given by;

c ≈ 7 km per litre.