Question

assume that the readings on the thermometers are normally distributed with a mean of 0° and standard deviation of 1.00°c. a thermometer is randomly selected and tested. draw a sketch and find the temperature reading corresponding to p93, the 93rd percentile. this is the temperature reading separating the bottom 93% from the top 7%. click to view page 1 of the table. click to view page 2 of the table. which graph represents p93? choose the correct graph below. the temperature for p93 is approximately (round to two decimal places as needed.)

Explanation:

Step1: Recall z - score formula for normal distribution

For a normal distribution $X\sim N(\mu,\sigma^{2})$, the z - score is given by $z=\frac{x - \mu}{\sigma}$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $x$ is the value from the distribution. We want to find the z - score $z$ such that $P(Z

Step2: Use the standard normal table

Looking up the value 0.93 in the standard - normal table (the cumulative distribution function of the standard normal distribution $Z\sim N(0,1)$), we find the corresponding z - score. The closest value in the standard - normal table to 0.93 is 0.9306, which corresponds to a z - score of approximately $z = 1.48$.

Step3: Solve for $x$

Since $\mu = 0$ and $\sigma=1$, and $z=\frac{x - \mu}{\sigma}$, substituting the values we get $1.48=\frac{x - 0}{1}$, so $x = 1.48$.

For the graph of $P_{93}$, the correct graph is the one where the area to the left of the vertical line (representing the value of $P_{93}$) under the normal - curve is 0.93. This means the shaded area is on the left - hand side of the vertical line and the vertical line is to the right of the mean (since the mean of the standard normal distribution is 0).

Answer:

The correct graph is the one where the shaded area to the left of a vertical line (right of the mean) under the normal curve is 0.93.
The temperature for $P_{93}$ is approximately $1.48$