MATH SOLVE

4 months ago

Q:
# 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

Accepted Solution

A:

The mean time in hours per day for newborn babies is 16.5 hours ⇒ DStep-by-step explanation:A sleep time of 15.9 hours per day for a newborn baby is at the 10thpercentile of the distribution of sleep times for all newborn babiesAssuming the distribution is normal with a standard deviation of 0.5 hourTo find the mean time let us do that1. Use the normal distribution table to find the corresponding z-score for 10th percentile2. Use the rule μ = x - zσ, where μ is the mean, σ is the standard deviation and x is the score3. Substitute the values of x, σ and z in the rule to find μLook to the normal distribution table to find z-score that equivalent to the area = 10/100 = 0.1 (10th percentile)∵ z-score = -1.28∵ σ = 0.5 hour∵ x = 15.9∵ μ = x - zσ- Substitute the values in the rule∴ μ = 15.9 - (-1.28)(0.5)∴ μ = 15.9 + 0.64∴ μ = 16.54 ≅ 16.5 hoursThe mean time in hours per day for newborn babies is 16.5 hoursLearn more:You can learn more about the normal distribution curve in brainly.com/question/8799684#LearnwithBrainly