The respiratory rate per minute in newborns varies according to a distribution t
ID: 3126311 • Letter: T
Question
The respiratory rate per minute in newborns varies according to a distribution that is approximately Normal with mean 51 and standard deviation 8. 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).
Explanation / Answer
a) It is between 2 standard deviations above and below the mean, so between
51 - 2*8 and 51 + 2*8
or
35 and 67 [ANSWER]
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b)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 55
u = mean = 51
s = standard deviation = 8
Thus,
z = (x - u) / s = 0.5
Thus, using a table/technology, the right tailed area of this is
P(z > 0.5 ) = 0.308537539 [ANSWER]
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c)
We first get the z score for the two values. As z = (x - u) / s, then as
x1 = lower bound = 40
x2 = upper bound = 55
u = mean = 51
s = standard deviation = 8
Thus, the two z scores are
z1 = lower z score = (x1 - u)/s = -1.375
z2 = upper z score = (x2 - u) / s = 0.5
Using table/technology, the left tailed areas between these z scores is
P(z < z1) = 0.084565722
P(z < z2) = 0.691462461
Thus, the area between them, by subtracting these areas, is
P(z1 < z < z2) = 0.606896739 [ANSWER]
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