This question demonstrates what can happen if you use rounded numerical results too soon. Always keep enough digits in intermedi

This question is poorly phrased

Complete Question

The lifespans of lions at a specific zoo follow a normal distribution. The average lifespan is 12.5 years with a standard deviation of 2.4 years. Apply the empirical rule (68-95-99.7%) to estimate the likelihood of a lion living between 5.3 and 10.1 years.

Answer:

The likelihood of a lion living from 5.3 to 10.1 years is 0.1585

Step-by-step explanation:

According to the empirical rule:

1) 68% of the data falls within 1 standard deviation of the mean, meaning between μ - σ and μ + σ.

2) 95% of the data is contained within 2 standard deviations around the mean - between μ - 2σ and μ + 2σ.

3) 99.7% of the data lies within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.

The mean provided is: 12.5

Standard deviation: 2.4 years

Starting with the first rule:

1) 68% falls within 1 standard deviation from the mean, implying between μ - σ and μ + σ.

μ - σ

12.5 - 2.4

= 10.1

We now apply the second rule:

2) 95% of the data lies within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.

μ – 2σ

12.5 - 2 × 2.4

12.5 - 4.8

= 7.7

Now applying the last rule:

3)99.7% of the data resides within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.

μ - 3σ

= 12.5 - 3(2.4)

= 12.5 - 7.2

= 5.3

The calculations indicate that

5.3 years is at one side of 99.7%

Therefore,

100 - 99.7%/2 = 0.3%/2

= 0.15%

Moreover, 10.1 years corresponds to one side of 68%

Thus

100 - 68%/2 = 32%/2 = 16%

Consequently, the percentage of a lion living between 5.3 to 10.1 years is evaluated as 16% - 0.15%

= 15.85%

Thus, the estimated probability of a lion surviving between 5.3 and 10.1 years

is represented as a decimal =

= 15.85/ 100

= 0.1585

There are 0.015 kilograms in 15 grams. Since each can weighs 0.015 kg and the payment rate is 50p per kilogram, 0.015 multiplied by 66 amounts to 1 kilogram! Therefore, 66 cans are needed to generate one kilogram. As a result, earning £15 would mean that with 2 kg equating to one dollar, then 15 multiplied by 2 equals 30. Consequently, 66 times 30 gives 1980!

66 relates to each kilogram, and 30 indicates how many 50p are required for one dollar!

Thus, to obtain £15, Adam has to recycle a total of 1980 cans!

To round the figure 47,125 to the closest tenth, hundredth, and thousandth, it's essential to recognize the positions of these places. The tens position is the second digit from the right. The hundreds position is the third, and the thousands position is the digit immediately following the comma. For rounding to the tens place, you must inspect the digit directly behind it (the ones place) and evaluate. If this digit is between 0-4, you won’t round the tens place, but if it falls between 5-9, rounding is permissible. The same regulation applies when rounding up for the hundreds and thousands places. Consequently, the number arrived at is - 47,135. 

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