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2 answers:
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Answer:
{13.7756,18.2244}
Step-by-step explanation:
Given the sample size, the margin of error can be calculated with the formula where Z is the critical value for the desired confidence level, σ is the population standard deviation, and n is the sample size. Therefore, our margin of error for a 90% confidence level is:
The formula for a confidence interval is where x-bar is the sample mean. Therefore, the 90% confidence interval for the mean amount of sushi pieces a person can eat is:
Therefore, we are 90% confident that the true mean amount of sushi pieces a person can eat is contained within the interval {13.7756,18.2244}
Hope that helps and hope you get better!
Answer:
0.0326 = 3.26% probability that a randomly selected thermometer reads between −2.23 and −1.69.
The sketch is drawn at the end.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Mean of 0°C and a standard deviation of 1.00°C.
This means that
Find the probability that a randomly selected thermometer reads between −2.23 and −1.69
This is the p-value of Z when X = -1.69 subtracted by the p-value of Z when X = -2.23.
X = -1.69
has a p-value of 0.0455
X = -2.23
has a p-value of 0.0129
0.0455 - 0.0129 = 0.0326
0.0326 = 3.26% probability that a randomly selected thermometer reads between −2.23 and −1.69.
Sketch:
