Answer:
b) falls between 18.4 and 31.6 minutes.
Step-by-step explanation:
Problems involving normally distributed samples can be tackled using the z-score formula.
In any set with a mean and standard deviation
, the z-score for a measurement X is calculated as follows:
The Z-score indicates how many standard deviations an observation diverges from the mean. After determining the Z-score, consulting the z-score table provides the associated p-value. This p-value represents the likelihood of observing a measure less than X, i.e., the percentile of X. Subtracting the p-value from 1 yields the probability of observing a measure greater than X.
In this question, we find that:
To cover the Middle 90%
The lower limit is determined as the value of X when Z corresponds to a p-value of 0.5 - 0.9/2 = 0.05.
The upper limit corresponds to the value of X when Z has a p-value of 0.5 + 0.9/2 = 0.95.
Lower limit:
X when Z = -1.645
X when Z = 1.645
Thus, the correct assessment is:
b) between 18.4 and 31.6 minutes.