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WINSTONCH [101]
3 years ago
5

Assume the upper arm length of males over 20 years old in the United States is approximately Normal with mean 39.2 centimeters (

cm) and standard deviation 2.2 cm. Use the 68–95–99.7 rule to answer the given questions. (a) What range of lengths covers almost all, 99.7% , of this distribution? Enter your answers rounded to one decimal place.
Mathematics
1 answer:
MAVERICK [17]3 years ago
3 0

Answer:

The interval [32.6 cm, 45.8 cm]

Step-by-step explanation:

According with the <em>68–95–99.7 rule for the Normal distribution:</em>  If \large \bar x  is the mean of the distribution and s the standard deviation, around 68% of the data must fall in the interval

\large [\bar x - s, \bar x +s]

around 95% of the data must fall in the interval

\large [\bar x -2s, \bar x +2s] 

around 99.7% of the data must fall in the interval

\large [\bar x -3s, \bar x +3s]

So, the range of lengths that covers almost all the data (99.7%) is the interval

[39.2 - 3*2.2, 39.2 + 3*2.2] = [32.6, 45.8]

<em>This means that if we measure the upper arm length of a male over 20 years old in the United States, the probability that the length is between 32.6 cm and 45.8 cm is 99.7%</em>

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