Answer
The probability that a randomly selected thermometer reads between -1.11 and -0.57 = 0.151
Step-by-step explanation
For probability questions that involve normal distribution, we usually convert the values to standardized forms or z-scores.
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ
So, to find the probability that the thermometer reading reads between -1.11 and -0.57 can be written as P (-1.11 < x < -0.57)
We first convert -11 and -0.57 into their z-score forms.
z = (x - μ)/σ
For -1.11
x = -1.11°C
μ = 0°C
σ = 1.00°C
z = (x - μ)/σ = (-1.11 - 0)/1 = -1.11
For -0.57
x = -0.57°C
μ = 0°C
σ = 1.00°C
z = (x - μ)/σ = (-0.57 - 0)/1 = -0.57
So,
P(-1.11 < x < -0.57)
= P(-1.11 < z < -0.57)
= P(z < -0.57) - P(z < -1.11)
Using the normal distribution table or the normal distribution calculator
= P(z < -0.57) - P(z < -1.11)
= 0.284 - 0.133
= 0.151
Hope this Helps!!!