20 hours put into degrees?
1 answer:
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Answer:
a) 11.51% probability that a random college woman has a height of 68 inches or more
b) This height is 70.135 inches.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
The normal distribution has two parameters, which are the mean and the standard deviation.
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 random college woman has a height of 68 inches or more?
This is 1 subtracted by the pvalue of Z when X = 68. So
has a pvalue of 0.8849
1 - 0.8849 = 0.1151
11.51% probability that a random college woman has a height of 68 inches or more
b. To be in the Tall Club, a woman must have a height such that only 2% of women are taller. What is this height?
This weight is the 100-2 = 98th percentile, which is the value of X when Z has a pvalue of 0.98. So X when Z = 2.054.
This height is 70.135 inches.