Question

Assume that the readings on the thermometers are normally distributed with a mean of 0 degrees and standard deviation of 1.00degreesC. A thermometer is randomly selected and tested. Draw a sketch and find the temperature reading corresponding to Upper P 88​, the 88 th percentile. This is the temperature reading separating the bottom 88 % from the top 12 %.

Answer 1

Answer:

1.18°

Step-by-step explanation:

Draw the normally distributed curve as in the image attached.

The value corresponding to the percentile can be found using the z-score.

The z-score table can be used in reverse order. After locating 88% or rather 0.88(or as close to it as possible) because the table is in decimals not percentages.

Back Calculating the z score

88% corresponds to a z score of 1.18

z score formula:

$z=\frac{x-mean}{Standard Deviation}$

Substituting z, then x can be solved as 1.18°

Answer 2

Using the normal distribution, we have that the 88th percentile is of 1.175ºC.

In a normal distribution with mean $\mu$ and standard deviation $\sigma$, the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

• It measures how many standard deviations the measure is from the mean.
• After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of measure X.

In this problem:

• Mean of 0ºC, thus $\mu = 0$
• Standard deviation of 1ºC, thus $\sigma = 1$

The 88th percentile is X when Z has a p-value of 0.88, so X when Z = 1.175. Then:

$Z = \frac{X - \mu}{\sigma}$

$1.175 = \frac{X - 0}{1}$

$X = 1.175$

The 88th percentile is of 1.175ºC.

The sketch is given at the end of this answer.

A similar problem is given at https://brainly.com/question/13025772