Question

assume the readings on thermometers are normally distributed with a mean of ( 0 ^ { circ } mathrm { c } ) and a standard deviation of ( 1.00 ^ { circ } mathrm { c } ). find the probability that a randomly selected thermometer reads between - 1.88 and - 1.19 and draw a sketch of the region. click to view page 1 of the table. click to view page 2 of the table. sketch the region. choose the correct graph below. the probability is ( square ). (round to four decimal places as needed.)

Explanation:

Step1: Find the cumulative probability for \(z = - 1.19\)

Using the standard normal distribution table, \(P(Z < - 1.19)=0.1170\)

Step2: Find the cumulative probability for \(z=-1.88\)

Using the standard normal distribution table, \(P(Z < - 1.88)=0.0301\)

Step3: Calculate the probability between the two \(z\) - values

We use the formula \(P(-1.88<Z < - 1.19)=P(Z < - 1.19)-P(Z < - 1.88)\)
Substitute the values: \(0.1170 - 0.0301=0.0869\)

Answer:

\(0.0869\)