The table shows Emma's midyear exam results. The exam results for each subject are normally distributed with the mean $\mu$ and standard deviation $\sigma$ shown in the table.

$$\begin{matrix} \text{Subject} & \text{Emma's score} & {\mu} & {\sigma}\\ \text{English} & \text{48} & \text{40} & \text{4.4}\\ \text{Mandarin} & \text{81} & \text{60} & \text{9}\\ \text{Geography} & \text{84} & \text{55} & \text{18}\\ \text{Biology} & \text{68} & \text{50} & \text{20}\\ \text{Maths} & \text{84} & \text{50} & \text{15}\\ \end{matrix}$$

Arrange Emma's subjects from 'best' to 'worst' in terms of the z-scores.

Which statement about retrospective and prospective toxicity studies is correct? (a) Retrospective studies are not conducted on humans. (b) Prospective studies are only conducted on wild animals. (c) Retrospective studies monitor health effects from future chemical exposures. (d) Prospective studies monitor health effects from future chemical exposures. (e) Prospective studies monitor health effects from past chemical exposures.

The table shows Emma's midyear exam results. The exam results for each subject are normally distributed with the mean $\mu$ and standard deviation $\sigma$ shown in the table.

$$\begin{matrix} \text{Subject} & \text{Emma's score} & {\mu} & {\sigma}\\ \text{English} & \text{48} & \text{40} & \text{4.4}\\ \text{Mandarian} & \text{81} & \text{60} & \text{9}\\ \text{Geography} & \text{84} & \text{55} & \text{18}\\ \text{Biology} & \text{68} & \text{50} & \text{20}\\ \text{Maths} & \text{84} & \text{50} & \text{15}\\ \end{matrix}$$

Find the z-score for each of Emma's subjects.

The weights of Jason's oranges are normally distributed. 84% of the crop weigh more than 152 grams and 16% weigh more than 200 grams. What percentage of the oranges weigh between 152 grams and 224 grams?

The weights of Jason's oranges are normally distributed. 84% of the crop weigh more than 152 grams and 16% weigh more than 200 grams. Find $\mu$ and $\sigma$ for the crop.

A bottle filling machine fills an average of 20000 bottles a day with a standard deviation of 2000. Assuming that production is normally distributed and the year comprises 260 working days, calculate the approximate number of working days on which: between 18000 and 24000 bottles (inclusive) are filled.

(a.) What is meant by tangent line approximation? (b.) Define the terms propagated error, relative error, and percentage error.

A bottle filling machine fills an average of 20000 bottles a day with a standard deviation of 2000. Assuming that production is normally distributed and the year comprises 260 working days, calculate the approximate number of working days on which: over 16000 bottles are filled

A bottle filling machine fills an average of 20000 bottles a day with a standard deviation of 2000. Assuming that production is normally distributed and the year comprises 260 working days, calculate the approximate number of working days on which: under 18000 bottles are filled

The height of male students in a university is normally distributed with mean 170 cm and standard deviation 8 cm. Find the value of k such that 16% of the students are taller than k cm.

The height of male students in a university is normally distributed with mean 170 cm and standard deviation 8 cm. Find the percentage of male students whose height is: (i) between 162 cm and 170 cm (ii) between 170 cm and 186 cm.

Write the word sentence as an inequality. $y+5 \gt 8 ; y=1$

Simplify.

$$\sqrt [ 3 ] { 32 }$$

Determine whether the given random variable X is discrete or continuous. X measures the living area of a randomly selected house in your neighborhood.