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Grace [21]
3 years ago
12

Assume that the readings on the thermometers are normally idistributed with a mean of 0◦ and a standard deviation of 1.00◦C. Fin

d P25, the 25th percentile. This is the temperature reading separating the bottom 25 % from the top 75 %
Mathematics
1 answer:
Karolina [17]3 years ago
7 0

Answer:

This temperature reading is -0.675ºC.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

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:

Assume that the readings on the thermometers are normally distributed with a mean of 0◦ and a standard deviation of 1.00◦C. This means that \mu = 0, \sigma = 1

Find P25, the 25th percentile.

This is the value of X when Z has a pvalue of 0.25. So we use Z = -0.675, since this happens between Z = -0.67 and Z = -0.68.

Z = \frac{X - \mu}{\sigma}

-0.675 = \frac{X - 0}{1}

X = -0.675

This temperature reading is -0.675ºC.

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