Answer:
a) 0.1020
b) 0.7125
c) 7.64 hours
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
(a) What is the probability that a visually impaired student gets less than 6.2 hours of sleep?
This is the pvalue of Z when X = 6.2. So
has a pvalue of 0.1020.
So the answer for a is 0.1020.
(b) What is the probability that a visually impaired student gets between 6.8 and 10.93 hours of sleep?
This is the pvalue of Z when X = 10.93 subtracted by the pvalue of Z when X = 6.8. So
X = 10.93
has a pvalue of 0.8810.
X = 6.8
has a pvalue of 0.1685.
So the answer for b) is 0.8810 - 0.1685 = 0.7125.
(c) Thirty percent of students get less than how many hours of sleep on a typical day?
This is the value of X in the 30th percentile, that is, the value of X when Z has a pvalue of 0.30. So it is X when Z = -0.525, since this happens between Z = -0.53 and Z = -0.52.
The answer for c is 7.64 hours.