The respiratory rate per minute in newborns varies according to a distribution t

Question

The respiratory rate per minute in newborns varies according to a distribution that is approximately Normal with mean 49 and standard deviation 6. Use this information to answer the following questions.

(a) Use the Empirical Rule: approximately 95% of all newborn respiratory rates per minute are between _ and _? . Please use whole numbers.

(b) The probability that a randomly chosen newborn has a respiratory rate of 55 per minute or more is _? . Please use 4 decimal places.

(c) The probability that a randomly chosen newborn has a respiratory rate per minute between 40 and 55 is approximately _? . Please use 4 decimal places.

Please show work and explain please.

Explanation / Answer

The respiratory rate per minute in newborns varies according to a distribution that is approximately Normal with mean 49 and standard deviation 6. Use this information to answer the following questions.

(a) Use the Empirical Rule: approximately 95% of all newborn respiratory rates per minute are between 37 and 61 . Please use whole numbers.

Approximately 95% of the data falls within two standard deviations of the mean (or between the mean – 2 times the standard deviation, and the mean + 2 times the standard deviation)

Mean -2sd =49-2*6=37

Mean +2sd =49+2*6=61

(b) The probability that a randomly chosen newborn has a respiratory rate of 55 per minute or more is _? . Please use 4 decimal places.

Z value for 55, z=(55-49)/6 =1

P(x >55) = P( z >1)

=0.1587

(c) The probability that a randomly chosen newborn has a respiratory rate per minute between 40 and 55 is approximately _? . Please use 4 decimal places.

Z value for 40, z=(40-49)/6 = -1.5

P( 40<x<55) =P( -1.5 <z <1)

P( z <-1.5) – P( z < 1)

= 0.8413 - 0.0668

= 0.7745

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