2. According to Center for Disease Control and Prevention (http://www.cdc.gov/),
ID: 3242809 • Letter: 2
Question
2. According to Center for Disease Control and Prevention (http://www.cdc.gov/), the mean
length of a six-month old American girls is about 65.73 cm and the standard deviation is
about 2.27 cm.
(a) Find the 5th percentile and the 95th percentile.
(b) A simple random sample of 50 six-month old girls’s growth records were selected from a
certain city. Assuming that this city’s environment is not different from the national average,
find the 5th and the 95th percentiles for the probability distribution of the sample mean.
Explanation / Answer
a) The Standard Normal Variate is Z = (X - Mean) / SD
gvien mean = 65.73 and sd = 2.2.7
From the standard norma table, Z5% = -1.645
The 5th percentile is X = Mean + Z5% * SD
= 65.73 -1.645*2.27 = 61.996
From the standard norma table, Z95% = 1.645
The 95th percentile is X = Mean + Z95% * SD
= 65.73 +1.645*2.27 = 69.464
b) Given sample size n = 50
The 5th percentile is X = Mean - Z5% * (SD / sqrt(n) )
= 65.73 -1.645* (2.27 / sqrt(50)) = 65.202
From the standard norma table, Z95% = 1.645
The 95th percentile is X = Mean + Z5% * (SD / sqrt(n) )
= 65.73 + 1.645* (2.27 / sqrt(50)) = 66.258
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