Use the mapping to determine which of the following are elements of the range.
1 answer:
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Answer:
a = 33.32
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:
P(32 < x < a) = .0590
This is the pvalue of Z when X = a subtracted by the pvalue of Z when X = 32.
X = 32
has a pvalue of 0.1587
X = a
p - 0.1587 = 0.0590
p = 0.0590 + 0.1587
p = 0.2177
So when X = a, Z has a pvalue of 0.2177. So when X = a, Z = -0.78.
So a = 33.32
Answer:
Hence the 90% confidence interval estimate of the population mean is
Step-by-step explanation:
Given that,
Point estimate = sample mean = = 88.34
sample standard deviation = s = 19.22
sample size = n = 14
Degrees of freedom = df = n - 1 = 13
Critical value = df = 1.771
Margin of error
Margin of error = E = 9.10
The 90% confidence interval estimate of the population mean is,