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A sleep time of 15.9 hours per day for a newborn baby is at the 10h percentile of the distribution of sleep times for all newborn babies. Assuming the distribution is normal with a standard deviation of 0.5 hour, approximately what is the mean time, in hours per day, for newborn babies?
A. 15.1
B. 15.3
Ğ¡. 16.3
D. 16.5
E. 16.7

Respuesta :

Answer:

option (D) 16.5

Step-by-step explanation:

Data provided:

Sleep time of , X = 15.9 is at the 10th percentile

Standard deviation, σ = 0.5  hour

also,

10th percentile of normal distribution is

Z = F⁻¹(0.10)

or

Z = - 1.28  (Using Standard Normal distribution)

Now,

[tex]\\Z=\frac{X-\mu}{\sigma}[/tex]

or

X = μ + ( σ × Z )

or

μ = X - ( σ × Z )

on substituting the respective values, we get

μ = 15.9 - 0.5 × (-1.28)

or

μ = 16.5

Hence, the correct answer is option (D) 16.5