HEG GenΓ¨ve APPLIED STATISTICS Β· WEEK 4 ← Course
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πŸ”§ Week 4 is in preparation. What follows is the plan for the 3-hour session β€” objectives, the Part 1 sections, the Part 2 exercise outline and the slide outline. Nothing here is counted yet.
Week 4 · Applied Statistics · HEG Genève

How long until the pizza reaches the table?

Counting things gave you the binomial. Measuring things β€” delivery time, dough weight, daily takings β€” needs a different object: a density, where probability is area. This week is the normal distribution end to end: the standard normal table, standardising, tails, and reading the table backwards to find the value behind a percentile.

🏫 In class: 3 h Β· lesson ~1 h, then exercises ~2 h πŸ“– Saylor ch. 5 β–Ά The Lecture button shows the slide outline

By the end of Week 4 you will be able to

  • Explain why P(X = x) is zero for a continuous variable and why probability is area under a density.
  • Use the standard normal table for P(Z < z), P(Z > z) and P(a < Z < b).
  • Standardise a general normal variable, z = (x βˆ’ Β΅)/Οƒ, and compute probabilities for delivery times.
  • Find the value x behind a tail area β€” the 95th percentile of delivery time β€” by reading the table backwards.
  • Recognise zβ‚€.β‚€β‚… and zβ‚€.β‚€β‚‚β‚… as the numbers Weeks 6–7 will use constantly.

Resources

βœ“Saylor Β§5.1 β€” Continuous random variables β†—
βœ“Saylor Β§5.2 β€” The standard normal distribution β†—
βœ“Saylor Β§5.3 β€” Probability computations for general normal random variables β†—
βœ“Saylor Β§5.4 β€” Areas of tails of distributions β†—
Homework for this week is written with the week itself, on the Week 1–2 pattern: a fresh dataset, hints and worked solutions.
Tools for this week
The shape of uncertainty β€” the normal, the bell, the tailsExam cards c2 and c6
← Course page
Section 4.1 Β· The hook

Under twelve minutes?

Planned Β· Hook

Estimate the share of pizzas served within 12 minutes

  • Slider: "delivery-to-table time averages 14 min with SD 3 β€” what share of pizzas arrive within 12?" Lock it; section 4.4 computes it.
Status β†’ this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.
Section 4.2 Β· Density

Probability is area

Planned Β· Concept

Continuous random variables and the uniform distribution (Β§5.1)

  • Widget: a uniform distribution of oven temperature drift; drag two bounds and read the area.
  • Why P(X = 14.000…) = 0 and why "between 13.9 and 14.1" is the only kind of question that has an answer.
Status β†’ this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.
Section 4.3 Β· The standard normal

The one curve that fits all

Planned Β· Table

P(Z < z) from the table (Β§5.2)

  • Widget: the standard normal curve; drag z and watch the shaded area and the table row highlight together.
  • Classify (6 rows): which area is asked β€” left tail, right tail, between β€” and how to get it from a left-tail table.
Status β†’ this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.
Section 4.4 Β· General normal

Standardise, then look up

Planned Β· Standardise

z = (x βˆ’ Β΅)/Οƒ for delivery times N(14, 3) (Β§5.3)

  • Widget: delivery times; type a time, see z, the area and the sentence "x% of pizzas arrive within…".
  • The hook closes: P(X < 12) with Β΅ = 14, Οƒ = 3. Exam card c6 ("normal distribution & inverse") is the drill.
Status β†’ this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.
Section 4.5 Β· Tails and the inverse

The value behind a percentile

Planned Β· Inverse

z_c, the 95th percentile, and the numbers Week 6 needs (Β§5.4)

  • Widget: choose a tail area (0.05, 0.025, 0.01) and read z_c off the curve; then un-standardise to a delivery time the pizzeria can promise: "95% of pizzas within __ minutes".
  • Introduce zβ‚€.β‚€β‚‚β‚… = 1.96 as a number to know by heart β€” it returns in every confidence interval.
Status β†’ this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.
Section 4.6 Β· Checkpoint

Prove it to yourself

Planned Β· Quiz

Self-check quiz & where this goes next

  • Ten questions: area = probability, left/right/between areas, standardising, an inverse lookup, and one uniform-distribution question.
Status β†’ this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.
Section 4.7 Β· Workshop

The pizzeria file Β· instalment four

Planned Β· Exercise

Workbook fields

  • w4_promise β€” the delivery promise you would print on the menu ("within __ minutes, 95% of the time") and the calculation behind it.
  • w4_normal β€” one quantity of your pizzeria you would model as normal, with a Β΅ and Οƒ you can justify, and one you would not.
Status β†’ this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.
Course page β†’
Part 2 · Exercises

8 exercises, worked together

Planned · ~94 min

The second half of the session

When this week is written, each exercise below becomes a form on this page and a slide in the deck, generated from one array so the two can never disagree — and its solution opens when the instructor reveals it in class. Same engine as Weeks 1–2 (exercises.js).

  • Exercise 1 Β· Area is probability  10 min
    a uniform density: read three areas
  • Exercise 2 Β· The z table, three ways  15 min
    P(Z < z), P(Z > z), P(a < Z < b)
  • Exercise 3 Β· Standardise  12 min
    delivery times N(14, 3): four probabilities
  • Exercise 4 Β· The hook closes: under twelve minutes  10 min
    P(X < 12), and what it means for the kitchen
  • Exercise 5 Β· Read the table backwards  15 min
    the 95th percentile of delivery time
  • Exercise 6 Β· zβ‚€.β‚€β‚… and zβ‚€.β‚€β‚‚β‚…  10 min
    the two numbers Weeks 6–7 use constantly
  • Exercise 7 Β· Normal or not?  10 min
    four quantities: which would you model as normal, and which not
  • Exercise 8 Β· The delivery promise  12 min
    write the menu line, with the calculation behind it
Status → outline only. Nothing here is interactive or counted yet.
Course page →