Question

1. Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading less than 1.089°C.

P(Z<1.089)=P(Z<1.089)=  (Round answer to four decimal places.)

2. Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading less than -1.5°C.

P(Z<−1.5)=P(Z<-1.5)=  (Round to four decimal places)

3. Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading greater than -3.225°C.

P(Z>−3.225)=P(Z>-3.225)=  (Round to four decimal places)

4. Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading greater than 1.254°C.

P(Z>1.254)=P(Z>1.254)=  (Round to four decimal places)

5. About % of the area under the curve of the standard normal distribution is outside the interval z=[−0.84,0.84]z=[-0.84,0.84] (or beyond 0.84 standard deviations of the mean).

(Notice that the percent sign is already there. Round to two decimal places.)

6. Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading between 0°C and 1.125°C.

P(0<Z<1.125)=P(0<Z<1.125)=  (Round to four decimal places)

Answer 1

Solution :

1)

P(z < 1.089) = 0.8619

Probability = 0.8619

2)

P(z < -1.5) = 0.0668

3)

P(z > -3.225) = 1 - 0.0006 = 0.9994

4)

P(z > 1.254) = 0.8951

5)

1 - P(-0.84 < z < 0.84) = 1 - 0.5991 = 0.4009 = 40.09%

6)

P(0 < z < 1.125) = P(z < 1.125) - P(z < 0) = 0.8697 - 0.5 = 0.3697