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maksim [4K]
4 years ago
5

Assume that the readings on the thermometers are normally distributed with a mean of 0 degrees0° and standard deviation of 1.00d

egrees°C. Assume 2.72.7​% of the thermometers are rejected because they have readings that are too high and another 2.72.7​% are rejected because they have readings that are too low. Draw a sketch and find the two readings that are cutoff values separating the rejected thermometers from the others.

Mathematics
1 answer:
Alex4 years ago
6 0

Answer:

The diagram is attached below.

Step-by-step explanation:

A normal distribution mean 0 and standard deviation 1 is known as the standard normal distribution.

So, the readings on the thermometers (denoted by <em>Z</em>) follows N (0, 1).

It is provided that 2.7​% of the thermometers are rejected because they have readings that are too high and 2.7​% are rejected because they have readings that are too low.

This implies that:

P(Zz)=0.027

The value of <em>z</em> associated to both these probabilities are:

<em>z</em> = 1.93.

That is,

P(Z1.93)=0.027

*Use a <em>z</em>-table.

The diagram for the two readings that are cutoff values separating the rejected thermometers from the others is attached below.

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