Question

Assume that thermometer readings are normally distributed with a mean of 100o F and a standard deviation of 0.15o F. a) Draw and label a sketch of the normal distribution of the thermometer readings. Include all pertinent data for the distribution b) A thermometer is randomly selected and tested. Find the probability that the thermometer reads between 99.86o F and 100.07o F. Draw a sketch of the distribution and shade the probability. Write out any calculator commands that you used.

Answer 1

The parameters of the normal distribution of the thermometer readings are its mean and the standard deviation

The probability that a thermometer reading is between 99.86o F and 100.07o F is 0.5403

The sketch of the normal distribution of the thermometer

The given parameters are:

• Mean, μ = 100
• Standard deviation, σ = 0.15

Next, we draw the normal distribution using a graphing calculator.

See attachment for the sketch of the normal distribution of the thermometer

The probability that a thermometer reading is between 99.86o F and 100.07o F

This means that:

x = 99.86 and x = 100.07

The probability is calculated as:

P(99.86 < x < 100.07) = P(x > 99.86) - P(x < 100.07)

Using the attached graph, we have:

P(99.86 < x < 100.07) = 0.5403

Read more about normal distribution at:

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