A sample of 20 students' scores on a statistics final exam are $62,65,67,68,70,71,72,73,74,75,76,77,78,79,80,81,82,83,85,88$. Does this sample suggest the scores are from a population that is approximately normal?

A team evaluating sustainable packaging wants to estimate the proportion of retail brands that use biodegradable materials in their products. Find the minimum sample size required for this estimate, assuming a $95\%$ confidence level and a margin of error of $0.10$. Earlier research indicates that around $70\%$ of retail brands have adopted biodegradable packaging.

A shipment of oranges has a population mean weight of $150$ grams and a standard deviation of $6$ grams. For a random sample of $n=64$ oranges, what is the probability that the sample mean weight is less than $150$ grams or greater than $151.5$ grams? Would a sample mean above $151.5$ grams be considered unusual?

A weather balloon records the following pairs of altitude in thousands of feet and temperature in ${}^{\circ }F$: $(1.5,60)$, $(3.8,52)$, $(6.0,44)$, $(8.2,35)$, and $(10.5,28)$. Find (a) the explained variation, (b) the unexplained variation.

A certain stock's daily percent return on Fridays has a mean of $3.12\%$ and a standard deviation of $41.25\%$. If random samples of $40$ days are selected and the mean return for each sample is calculated, what is the probability that a sample mean is between $-5\%$ and $10\%$?

The following are the cholesterol levels (in $\text{mg/dL}$) of $10$ randomly selected adults from a health survey. Assume the cholesterol levels are normally distributed. Construct a $99\%$ confidence interval for the population standard deviation.

Data: $180,190,195,200,210,220,225,230,240,250$