Lab 03

1. The weights of newborn babies in a certain hospital follow a normal distribution with:

Mean (μ) = 3.2kg Standard deviation (s) = 0.5kg Use this information to answer the following questions.

68% = $mu+-1\sigma$ 95% = $mu+-2\sigma$ 99.7% = $mu+-3\sigma$

a) Using the Empirical Rule, estimate the range of baby weights that includes the middle 68% of newborns.

b) What is the estimated weight range for the middle 95% of newborns?

c) Estimate the weight range for 99.7% of newborns. minimum range = 1.7 maximum range = 4.7

d) What percentage of newborns weigh less than 2.4kg?

$$\begin{array}{r}z=\frac{x-\mu }{\sigma }\\ z=\frac{2.4-3.2}{0.5}\\ z=-1.6\\ 0.9452\\ \text{percentage of newborns weigh less than 2.4kg}=1-0.9452=0.0548\end{array}$$

e) What percentage of newborns weigh more than 4.2kg?

$$\begin{array}{r}z=\frac{x-\mu }{\sigma }\\ z=\frac{4.2-3.2}{0.5}\\ z=2\\ 0.9772\\ \text{percentage of newborns weigh more than 4.2kg}=1-0.9772=0.0228\end{array}$$

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2. The following are the reaction times (in seconds) of 10 students in a cognitive response test:

2.8 3.1 2.5 3.0 2.7 3.4 2.9 3.2 2.6 3.3

a) Calculate the mean and standard deviation of the data.

$$\begin{array}{r}\mu =2.95\\ \sigma =\sqrt{\frac{(-29.5^2}{1}0}\\ 0.3028\end{array}$$

b) Using the values from a), use the Empirical Rule to estimate the range of scores that fall within 68%, 95% and 99.7%.

68% = 2.647 3.2528 95% = 3.25 3.5556 68% = 2.0416 3.8584

c) How many students in the dataset have scored that fall within 1 standard deviation of the mean?

students between range [2.6 → 3.3] 6 students scored that fall within 1 standard deviation

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3. Generate 100 random values from a standard normal distribution. Plot the QQ-plot and interpret whether the data is normally distributed.
4. Use mtcars dataset (built-in dataset in R). Plot a QQ-plot for the variable mpg and assess normality.
5. Use the iris dataset (built-in dataset in R). Plot a QQ-plot for the Sepal.Length variable and perform a Shapiro-Wilk test for normality.
6. Scenario: you are analyzing the iris dataset and want to compare whether the Sepal Length of 2 species – setosa and versicolor – follow similar distributions.