Question

question nine
given the following frequency distribution of model of cars in a car park, what is the mode?

car model	subaru	toyota	mazda	yukon	ford escape
frequency	12	23	5	8	25

question ten
iq scores are approximately bell - shaped with a mean of 80 and a standard deviation of 12.

a) between what two values will approximately 95% of the iq scores be within?

b) about what percent of the iq scores is between 68 and 92?

c) about what percent of the iq scores is between 44 and 116?

Explanation:

Step1: Recall mode definition

The mode is the value that appears most frequently in a data - set.

Step2: Identify highest frequency

In the car - model frequency distribution, the frequency of Ford escape is 25, which is the highest among all the frequencies (12 for Subaru, 23 for Toyota, 5 for Mazda, 8 for Yukon).

Step1: Recall the empirical rule for normal distribution

For a normal (bell - shaped) distribution, approximately 95% of the data lies within 2 standard deviations of the mean. The formula for the range is $\mu\pm2\sigma$, where $\mu$ is the mean and $\sigma$ is the standard deviation.

Step2: Calculate the lower and upper bounds

Given $\mu = 80$ and $\sigma=12$.
The lower bound is $\mu - 2\sigma=80 - 2\times12=80 - 24 = 56$.
The upper bound is $\mu + 2\sigma=80+2\times12=80 + 24 = 104$.

Step1: Calculate z - scores

The z - score formula is $z=\frac{x-\mu}{\sigma}$.
For $x = 68$, $z_1=\frac{68 - 80}{12}=\frac{- 12}{12}=-1$.
For $x = 92$, $z_2=\frac{92 - 80}{12}=\frac{12}{12}=1$.

Step2: Use the empirical rule

According to the empirical rule, approximately 68% of the data in a normal distribution lies within 1 standard deviation of the mean ($z=-1$ to $z = 1$).

Step1: Calculate z - scores

For $x = 44$, $z_1=\frac{44 - 80}{12}=\frac{-36}{12}=-3$.
For $x = 116$, $z_2=\frac{116 - 80}{12}=\frac{36}{12}=3$.

Step2: Use the empirical rule

According to the empirical rule, approximately 99.7% of the data in a normal distribution lies within 3 standard deviations of the mean ($z=-3$ to $z = 3$).

Answer:

Ford escape