Question

question 22 (1 point)
give an exact answer based on the empirical rule for the question given below.
the price paid for a particular model of hd television is approximately a normal distribution. the mean price paid is $1400 and the standard deviation is $135.
what is the approximate percentage of buyers who paid above $1,670?
your answer:
answer
question 23 (bonus) (1 point)
use the standard normal distribution table to answer the question below.
the average annual rainfall for a community has approximately a normal distribution. the mean rain fall is 41 inches and the standard deviation is 4 inches.
what is the approximate percentage of times we observe an annual rain fall amount below 37 inches?
______%
round the z - score to two decimal places if needed. give answer to two decimal places after converting to a percent. do not include the \%\ sign in your answer.
your answer:
answer

Explanation:

Step1: Calculate the z - score for Question 22

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x = 1670\), \(\mu=1400\), and \(\sigma = 135\).

$$z=\frac{1670 - 1400}{135}=\frac{270}{135}=2$$

According to the empirical rule, about \(95\%\) of the data lies within \(z=- 2\) and \(z = 2\). So the percentage of data outside \(z=-2\) and \(z = 2\) is \(100\%-95\% = 5\%\). Since the normal distribution is symmetric, the percentage of data above \(z = 2\) is \(\frac{5\%}{2}=2.5\%\)

Step2: Calculate the z - score for Question 23

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x = 37\), \(\mu = 41\), and \(\sigma=4\)

$$z=\frac{37 - 41}{4}=\frac{-4}{4}=-1$$

Looking up the z - score of \(-1\) in the standard normal distribution table, the cumulative probability \(P(Z\lt - 1)\) is \(0.1587\)

Answer:

Question 22: \(2.5\)
Question 23: \(15.87\)