Question

assume that thermometer readings are normally distributed with a mean of 0°c and a standard deviation of 1.00°c. a thermometer is randomly selected and tested. for the case below, draw a sketch, and find the probability of the reading. (the given values are in celsius degrees.)
between 0.50 and 1.75
click to view page 1 of the table. click to view page 2 of the table.
draw a sketch. choose the correct graph below.
a.
b.
c.
the probability of getting a reading between 0.50°c and 1.75°c is □.
(round to four decimal places as needed.)

Explanation:

Step1: Find the area corresponding to \(z = 0.50\)

Using the standard normal distribution table, the area to the left of \(z = 0.50\) is \(P(Z<0.50)=0.6915\)

Step2: Find the area corresponding to \(z = 1.75\)

Using the standard normal distribution table, the area to the left of \(z = 1.75\) is \(P(Z < 1.75)=0.9599\)

Step3: Calculate the probability between \(z = 0.50\) and \(z = 1.75\)

We use the formula \(P(0.50<Z<1.75)=P(Z < 1.75)-P(Z < 0.50)\)
Substitute the values: \(P(0.50<Z<1.75)=0.9599 - 0.6915\)
\(P(0.50<Z<1.75)=0.2684\)

Answer:

\(0.2684\)