Question

15 of 17 (13 complete) HW Score: 54.9%, 9.33 of 1 X6.1.27 Question Help Assume the readings on thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. Find the probability that a randomly selecte thermometer reads between - 1.11 and -0.57

Answer 1

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!!!