Complete Question
Assume the readings on thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.0°C. Find the probability that a randomly selected thermometer reads between 0.50°C and 1.50°C and draw a sketch of the region.
Answer:
0.24173
Step-by-step explanation:
We would solve this question using Z score formula.
z = (x-μ)/σ
where:
x is the raw score
μ is the population mean = 0°C
σ is the population standard deviation = 1°C
For x = 0.5°C
z = (0.5 - 0)/1
z = 0.5
Probability value from Z-Table:
P(x = 0.5) = 0.69146
For x = 1.5°C
z = (1.5 - 0)/1
z = 1.5
Probability value from Z-Table:
P(x = 1.5) = 0.93319
The probability of that a randomly selected thermometer reads between 0.50°C and 1.50°C is calculated as:
P(0.5 < Z < 1.5) = P(x = 1.5) - P(x = 0.5)
= 0.93319 - 0.69146
= 0.24173
Find attached to this answer the sketch of the region.
