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Answer:
11.51% probability of observing an 83 degree F temperature or higher LA during a randomly chosen day in June
The coldest 10% of the days during June in LA have high temperatures of 70.6F or lower.
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:
What is the probability of observing an 83 degree F temperature or higher LA during a randomly chosen day in June?
This probability is 1 subtracted by the pvalue of Z when X = 83. So
has a pvalue of 0.8849.
1 - 0.8849 = 0.1151
11.51% probability of observing an 83 degree F temperature or higher LA during a randomly chosen day in June
How cold are the coldest 10% of the days during June in LA?
High temperatures of X or lower, in which X is found when Z has a pvalue of 0.1, so whn Z = -1.28
The coldest 10% of the days during June in LA have high temperatures of 70.6F or lower.