Question

Multi part question needing assistance please.

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 greater than -1.378°C. P(Z>−1.378) _____________ ******* WHAT DO I DO ABOUT THE 8? I CAN SEE ON THE CHART THE -1.37 BUT DONT KNOW WHAT TO DO CONCERNING THE 8.

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 between 1.141°C and 2.549°C. P(1.141<Z<2.549) _______ ****HOW DO I DO TWO GIVEN NUMBERS?

3. About % of the area under the curve of the standard normal distribution is between z=−2.159 and z=2.159 (or within 2.159 standard deviations of the mean).

Answer 1

Let X denotes the reading at freezing on a randomly selected thermometer.

X ~ Normal(0, 1)

The probability of obtaining a reading greater than -1.378°C

2. The probability of obtaining a reading between 1.141°C and 2.549°C

3. The probability of obtaining a reading between -2.159°C and 2.159°C

The percentage of the area under the curve of the standard normal distribution is between z=−2.159 and z=2.159

= 100*P(-2.159 <=X <=2.159)

= 100*0.969150

= 96.915%