A sleep time of 15.9 hours per day for a newborn baby is at the 10th percentile of the distribution of sleep times for all newborn babies. Assuming the distribution is normal with standard deviation 0.5 hour, approximately what is the mean sleep time, in hours per day, for newborn babies?

The mean sleep time is 16.54 hours per day for newborn babies

Explanation:

* Lets explain how to solve the problem

Percentiles are used to compare data across a larger sample.

To calculate the percentile, you will need to know the score, the mean

and the standard deviation.

In the problem you have the percentile and you want to find the mean.

To do that we must find z-score for the percentile from the normal

distribution table.

If the percentile lower than the 50th percentile, you will get a negative

z-score.

z-score = (x - μ) / σ, where x is the score, μ is the mean and σ is the

standard deviation

A sleep time of 15.9 hours per day for a newborn baby

x = 15.9 hours

At the 10th percentile of the distribution of sleep times for all newborn

babies

That means we want to find z-score corresponding to 0.1 (10/100 = 0.1)

By using the normal distribution table

z = - 1.28

The standard deviation is 0.5 hour

σ = 0.5

Substitute these values in the rule above

-1.28 = (15.9 - μ) / 0.5

Multiply both sides by 0.5

-0.64 = 15.9 - μ

Add μ to both sides

-0.64 + μ = 15.9

add - 0.64 to both sides

μ = 15.9 + 0.64 = 16.54

The mean sleep time is 16.54 hours per day for newborn babies