Answer:
a) 20.33% probability that the participant is less than 64.5 inches.
b) 33.72% probability that the participant is more than 68.25 inches
Step-by-step explanation:
Problems of normally distributed samples are 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.) Find the probability that the participant is less than 64.5 inches?
This is the pvalue of Z when X = 64.5.
has a pvalue of 0.2033
20.33% probability that the participant is less than 64.5 inches.
b.) Find the probability that the participant is more than 68.25 inches?
This is 1 subtracted by the pvalue of Z when X = 68.25.
has a pvalue of 0.6628
1 - 0.6628 = 0.3372
33.72% probability that the participant is more than 68.25 inches