Question

Assume that the readings on thermometers in a room are normally distributed with mean 0∘ and standard deviation 1.00∘C. A thermometer is randomly selected and tested. Find the probability that the reading on the thermometer (in degrees Celsius) is

Answer 1

Answer:

(a) 0.4945.

(b) 0.3643.

(c) 0.5965.

(d) 0.0869.

(e) 0.9974.

Step-by-step explanation:

Let X = readings on thermometers in a room.

The random variable X follows a Normal distribution with mean, μ = 0°C and standard deviation, σ = 1.00°C.

(a)

Compute the probability that the reading on the thermometer is between 0°C an 2.54°C as follows:

$P(0$

*Use a z-table.

Thus, the probability that the reading on the thermometer is between 0°C an 2.54°C is 0.4945.

(b)

Compute the probability that the reading on the thermometer is between -1.10°C an 0°C as follows:

$P(-1.1$

*Use a z-table.

Thus, the probability that the reading on the thermometer is between -1.10°C an 0°C is 0.3643.

(c)

Compute the probability that the reading on the thermometer is between -0.38°C an 1.63°C as follows:

$P(-0.38$

*Use a z-table.

Thus, the probability that the reading on the thermometer is between -0.38°C an 1.63°C is 0.5965.

(d)

Compute the probability that the reading on the thermometer is less than -1.36°C as follows:

$P(X$

Thus, the probability that the reading on the thermometer is less than -1.36°C is 0.0869.

(e)

Compute the probability that the reading on the thermometer is greater than -2.79°C as follows:

$P(X>-2.79)=P(\frac{A-\mu}{\sigma}>\frac{-2.79-0}{1})=P(Z$

Thus, the probability that the reading on the thermometer is greater than -2.79°C is 0.9974.