Assume that thermometer readings are normally distributed with a mean of 0.0
and a standard deviation of 1,00. the thermometer is randomly selected and tested. For the case below, draw a sketch , and find the probability of the reading The given values in Celsius degrees)
Between -1.26 and 1.58
Cannot sketch on these posts.
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions/probabilities related to the Z scores.
To find the probability of a thermometer reading between -1.26 and 1.58, we need to determine the area under the normal distribution curve within this range.
1. Start by sketching the normal distribution curve. The mean is at 0.0, and the standard deviation is 1.00. The curve is symmetric around the mean.
2. Label the values -1.26 and 1.58 on the x-axis.
3. Use a standard normal distribution table or a calculator to find the z-scores corresponding to these values. The formula to calculate the z-score is:
z = (x - μ) / σ
where x is the value, μ is the mean, and σ is the standard deviation.
For -1.26:
z1 = (-1.26 - 0) / 1.00
z1 = -1.26
For 1.58:
z2 = (1.58 - 0) / 1.00
z2 = 1.58
4. Use the z-scores to find the probabilities associated with these values using either a standard normal distribution table or a calculator. The probability is the area under the curve between the z-scores.
P(-1.26 < X < 1.58) = P(-1.26 < Z < 1.58)
You can use a standard normal distribution table to find the corresponding probabilities for -1.26 and 1.58. The table provides the area to the left of the z-score.
P(-1.26 < Z < 1.58) = P(Z < 1.58) - P(Z < -1.26)
Look up the values in the table and subtract the smaller probability from the larger one.
5. Interpret the result as a probability. The resulting value will be the probability of a thermometer reading between -1.26 and 1.58.
Note: Make sure the z-scores are positive when using the standard normal distribution table. If you have negative z-scores, find the probability for their absolute values and subtract it from 1.