Question

In the following exercises, assuming that the thermometer readings are normally distributed, with a mean of 0 celsius and a standard deviation of 1.00 celsius. A thermometer is randomly selected and tested. In each case, calculate the probability of each reading.

to. greater than 1.25
b. greater than -1.75
c. less than 2.50
d. less than -3.75
and. between -2.45 and -2.00
F. between -1.00 and 4.00
g. P (-1.96 <z <1.96)

Answer 1

Solution :

Given that,  

Using standard normal table ,

a.

P(z > 1.25) = 1 - P(z < 1.25) = 1 - 0.8944 = 0.1056

b.

P(z > -1.75) = 1 - P(z < -1.75) = 1 - 0.0401 = 0.9599

c.

P(z < 2.50) = 0.9938

d.

P(z < -3.75) = 0.0001

and

P(-2.45 < z < -2.00)

= P(z < -2.00) - P(z < -2.45)

= 0.0228 - 0.0071

= 0.0217

P(-2.45 < z < -2.00) = 0.0217

f

P(-1.00 < z < 4.00)

= P(z < 4.00) - P(z < -1.00)

= 1 - 0.1587

= 0.8413

P(-1.00 < z < 4.00) = 0.8413

g

P(-1.96 < z < 1.96)

= P(z < 1.96) - P(z < -1.96)

= 0.975 - 0.025

= 0.95

P(-1.96 < z < 1.96) = 0.95