Question

This is a multi-part question.

First, find the following: For a standard normal distribution, find: P(-1.17 < z < 0.02)+__________

Second, resolve this: 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 -0.08°C.
P(Z<−0.08)= ____________

Third, resolve this: 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 -0.798°C and 0.461°C.
P(−0.798<Z<0.461)= ______________

Last, resolve this: About ______% of the area under the curve of the standard normal distribution is between z=−0.279z and z=0.279 (or within 0.279 standard deviations of the mean).

Answer 1

Solution(a)
P(-1.17<Z<0.02) can be calculated as
P(-1.17<Z<0.02) = P(Z<0.02) - P(Z<-1.17)
P-value can be find from Z table as follows
P(-1.17<Z<0.02) = P(Z<0.02) - P(Z<-1.17) = 0.5080 - 0.1210 = 0.387
Solution(b)
Given in the question
Mean = 0
Standard deviation = 1
We need to calculate
P(Z<-0.08), this can be calculated from Z table
P(Z<-0.08) = 0.4681
Solution(c)
P(-0.798<Z<0.461) = P(Z<0.461) - P(Z<-0.798) = 0.6776 - 0.2124 = 0.4652
Solution(d)
P(-0.279<Z<0.279) = P(Z<0.279) - P(Z<-0.279) = 0.6099 - 0.3901 = 0.2198