Question

Long jump Refer to Exercise $21$ Suppose that the corrected long-jump

distances are converted from centimeters to meters (note that $100cm=1m$ ).

a. What shape would the resulting distribution have? Explain your answer.

b. Find the mean of the distribution of corrected long-jump distance in meters.

c. Find the standard deviation of the distribution of corrected long-jump distance in meters.

Short answer

Part (a) The distribution is roughly symmetric along with a single peak.

Part (b) Mean of the distribution of the corrected long $-$jump distance is $5.573m$

Part (c) Standard deviation of the distribution of the corrected long $-$ jump distance is $0.04713m$

Step-by-step solution

Part (a) Step 1: Given information

$100cm=1m$

$\overline{x_N}=557.3cm$

To convert the corrected long jump distances from centimetres to metres, divide each centimetre number by $100$

Part (a) Step 2: Explanation

The geometry of the corrected long-jump distances in centimetres distribution was discovered to be a fairly symmetric distribution with a single peak.

When every value in the data is split by 100, the structure of the distribution remains unchanged because the associations between each data pair remain unchanged.

As a result, the shape of the corrected long-jump distances in metres distribution is also an approximately symmetric distribution with a single peak in this example.

Part (b) Step 1: Calculation

To convert the corrected long-jump distances from centimetres to metres, divide each centimetre number by $100$

Because the mean is the measure of the centre, when we divide every data value by $100$we must likewise divide the centre of the distribution by $100$

In the previous problem, we learned that the mean of the corrected long-jump distance distribution was $557.3cm$To convert the mean of the adjusted long-jump distance distribution from centimetres to metres, multiply the mean in centimetres by $100$

$\overline{x_N}=\frac{557.3}{100}=5.573m$

Thus,

The distribution of corrected long-jump distance in metres has a mean of$5.573m$

Part (c) Step 1: Calculation

We discovered that the standard deviation of the corrected long-jump distance distribution was $4.713m$We must divide the standard deviation in centimetres by $100$to transform the standard deviation of the distribution of corrected long-jump distances from centimetres to metres.

${SD}_N=\frac{4.713}{100}=0.04713m$

Thus,

The standard deviation of the adjusted long jump distance distribution in metres is$0.0473m$