Question

Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of

0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the
probability of obtaining a reading between 0.391°C and 0.768°C.
P(0.391 Z < 0.768) =

Answer 1

Explanation:

Z = (X - μ) / σWhere:X is the value you want to find the probability for,μ is the mean, and σ is the standard deviation.

For the lower bound (0.391°C): Z_lower = (0.391 - 0) / 1.00 = 0.391

For the upper bound (0.768°C): Z_upper = (0.768 - 0) / 1.00 = 0.768

Now, you want to find the probability that the Z-score falls between these values.

You can use a standard normal distribution table or calculator to find the probabilities associated with these Z-scores.

P(0.391 < Z < 0.768) = P(Z < 0.768) - P(Z < 0.391)

Using a standard normal distribution table or calculator, you can find the probabilities associated with these Z-scores. Subtract the smaller probability from the larger one to find the probability between the two values.

P(Z < 0.768) ≈ 0.7764 P(Z < 0.391) ≈ 0.6480

Now, subtract the smaller probability from the larger one:

P(0.391 < Z < 0.768) ≈ 0.7764 - 0.6480 ≈ 0.1284

So, the probability of obtaining a reading between 0.391°C and 0.768°C is approximately 0.1284, or 12.84%.

hope it helps