distribution (A-level only) Flashcards","topicId":"f9661294-95d4-42ef-9ff4-0bf0c7ac3086","topicSlug":"the-normal-distribution","cards":[{"id":"05070de9-b1bf-4de5-aa26-0ea08b8d3a16","cardType":"basic","front":"How is probability represented on a Normal curve?","back":"By the area under the curve, not its height.","points":1,"mcqOptions":null},{"id":"6101ee96-c49a-4589-8f73-0f4544688953","cardType":"basic","front":"What is the total area under a Normal curve?","back":"1.","points":1,"mcqOptions":null},{"id":"644f38d4-a952-4963-ab9e-039c14cc6451","cardType":"basic","front":"For a continuous random variable, what is $P(X=a)$?","back":"$0$.","points":1,"mcqOptions":null},{"id":"28ea9777-f706-4de2-9eb0-3340ea522e7a","cardType":"cloze","front":"If $X$ is Normally distributed, its notation is $\\text{[...]}$, where the second parameter is the variance.","back":"If $X$ is Normally distributed, its notation is $\\boxed{X\\sim N(\\mu,\\sigma^2)}$, where the second parameter is the variance.","points":null,"mcqOptions":null},{"id":"0789af71-7185-402d-9912-eb617394d64b","cardType":"cloze","front":"If $X$ is Normally distributed, its notation is $X\\sim N(\\mu,\\sigma^2)$, where the second parameter is the [ ].","back":"If $X$ is Normally distributed, its notation is $X\\sim N(\\mu,\\sigma^2)$, where the second parameter is the variance.","points":null,"mcqOptions":null},{"id":"8ab6eced-7613-4d5a-90e1-e2b4be8bbf34","cardType":"basic","front":"How does increasing $\\mu$ affect a Normal curve?","back":"It moves the entire curve to the right.","points":1,"mcqOptions":null},{"id":"b642141e-797d-4111-9142-a38aa06b254e","cardType":"basic","front":"How does increasing $\\sigma$ affect a Normal curve?","back":"It makes the curve wider and lower.","points":1,"mcqOptions":null},{"id":"3c93a2e0-8780-4934-9a3c-fc0648096cfc","cardType":"basic","front":"Where are the points of inflection of $N(\\mu,\\sigma^2)$?","back":"At $x=\\mu-\\sigma$ and $x=\\mu+\\sigma$.","points":1,"mcqOptions":null},{"id":"9b7cf5b9-1485-4401-9dfe-7ab522a6b83d","cardType":"basic","front":"Approximately what percentages lie within one, two and three standard deviations of the mean?","back":"

One: 68%
Two: 95%
Three: 99.7%

","points":3,"mcqOptions":null},{"id":"b27fc392-496f-418c-99c8-996684a35a1f","cardType":"basic","front":"Why does $P(X<a)=P(X\\le a)$ for a Normal variable?","back":"Because the endpoint has zero probability: $P(X=a)=0$.","points":2,"mcqOptions":null},{"id":"61302b82-3ead-4292-bb0d-005051b23654","cardType":"cloze","front":"Standardising $X\\sim N(\\mu,\\sigma^2)$ gives $\\text{[...]}$, with $Z\\sim N(0,1)$.","back":"Standardising $X\\sim N(\\mu,\\sigma^2)$ gives $\\boxed{Z=\\frac{X-\\mu}{\\sigma}}$, with $Z\\sim N(0,1)$.","points":null,"mcqOptions":null},{"id":"e1b68c97-845f-47f2-b720-2efbfd70a464","cardType":"cloze","front":"Standardising $X\\sim N(\\mu,\\sigma^2)$ gives $Z=\\frac{X-\\mu}{\\sigma}$, with $\\text{[...]}$.","back":"Standardising $X\\sim N(\\mu,\\sigma^2)$ gives $Z=\\frac{X-\\mu}{\\sigma}$, with $\\boxed{Z\\sim N(0,1)}$.","points":null,"mcqOptions":null},{"id":"b5b1d628-f319-42b0-bfd9-a33d7b98f03b","cardType":"basic","front":"What does a negative z-score show?","back":"The value is below the mean.","points":1,"mcqOptions":null},{"id":"b3da35d4-8f58-4d1a-a0cc-b7733e41457e","cardType":"basic","front":"For $X\\sim N(1200,150^2)$, what is the z-score of 990?","back":"$z=-1.4$.","points":1,"mcqOptions":null},{"id":"483e03af-40b9-4cf4-9e53-578b9096bd5a","cardType":"basic","front":"How can $P(X>a)$ be found using a lower-tail probability?","back":"$P(X>a)=1-P(X<a)$.","points":1,"mcqOptions":null},{"id":"3b8c8e8b-0cfd-4fdb-b419-4f8f77876c2d","cardType":"basic","front":"If only 10%

2.4.2 The Normal distribution (A-level only) Flashcards

2.4.2 The Normal distribution (A-level only) Flashcards