Question

question 16 (bonus) (1 point)
use the standard normal distribution table to help answer the question below.
scores are normally distributed with a mean of 10 and standard deviation of 7.
what is the approximate percentage of times we observe a score below 14?
______%
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
question 17 (bonus) (1 point)
use the standard normal distribution table to answer the question below.
scores are normally distributed with a mean of 20 and standard deviation of 3.
what is the approximate percentage of times we observe a score above 18?
______%
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 16

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x = 14\), \(\mu=10\), and \(\sigma = 7\).

$$z=\frac{14 - 10}{7}=\frac{4}{7}\approx0.57$$

Step2: Find the probability for Question 16

Using the standard normal distribution table, for \(z = 0.57\), the cumulative probability \(P(Z<0.57)\) is \(0.7157\) (from the table).

Step3: Calculate the z - score for Question 17

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x = 18\), \(\mu = 20\), and \(\sigma=3\).

$$z=\frac{18 - 20}{3}=\frac{-2}{3}\approx - 0.67$$

Step4: Find the probability for Question 17

Using the standard normal distribution table, \(P(Z < - 0.67)=0.2514\). Then \(P(Z> - 0.67)=1 - P(Z < - 0.67)\)

$$P(Z> - 0.67)=1-0.2514 = 0.7486$$

Answer:

71.57
74.86