Eureka is a weather station in the state of California and Seabrook is a weather station in the state of Massachusetts. On one summer day, the noon temperature recorded at Eureka was 24° Celsius, and the noontime temperature recorded at Seabrook was 27° Celsius. On that same day, the noontime temperatures at weather stations in California had a population mean of 39.2° Celsius and a standard deviation of Also on that day, the noontime temperatures at weather stations in Massachusetts had a population mean of 29.9° Celsius and a standard deviation Celsius. On the summer day, each state's distribution of noontime temperatures at its weather stations was clearly bell-shaped. (a) Find the z-scores of Eureka's noontime temperature on the summer day as a weather station in California and

Eureka is a weather station in the state of California and Seabrook is a weather station in the state of Massachusetts. On one summer day, the noon temperature recorded at Eureka was 24° Celsius, and the noontime temperature recorded at Seabrook was 27° Celsius. On that same day, the noontime temperatures at weather stations in California had a population mean of 39.2° Celsius and a standard deviation of Also on that day, the noontime temperatures at weather stations in Massachusetts had a population mean of 29.9° Celsius and a standard deviation Celsius. On the summer day, each state's distribution of noontime temperatures at its weather stations was clearly bell-shaped. (a) Find the z-scores of Eureka's noontime temperature on the summer day as a weather station in California and

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Description: Eureka is a weather station in the state of California and Seabrook is a weather station in the state of Massachusetts. On one summer day, the noontimetemperature recorded at Eureka was 24° Celsius, and the noontime temperature recorded at Seabrook

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Concept explainers

Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.

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Question

Eureka is a weather station in the state of California and Seabrook is a weather station in the state of Massachusetts. On one summer day, the noontime
temperature recorded at Eureka was 24° Celsius, and the noontime temperature recorded at Seabrook was 27° Celsius.
On that same day, the noontime temperatures at weather stations in California had a population mean of 39.2° Celsius and a standard deviation of 4.4° Celsius.
Also on that day, the noontime temperatures at weather stations in Massachusetts had a population mean of 29.9° Celsius and a standard deviation of 1.1°
Celsius. On the summer day, each state's distribution of noontime temperatures at its weather stations was clearly bell-shaped.
(a) Find the z-scores of Eureka's noontime temperature on the summer day as a weather station in California and
Seabrook's noontime temperature on the summer day as a weather station in Massachusetts. Round your answers to
two decimal places.
z-score of Eureka's noontime temperature: I
z-score of Seabrook's noontime temperature:|
(b) Relative to its population, which weather station had the lower noontime temperature?
Choose the best answer based on the z-scores of the two noontime temperatures.
Eureka
Seabrook
It is unclear which weather station had the lower noontime temperature relative to its
population
SEP
3.
DD

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