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Quiz

The normal distribution

sophie waddington 11 Fragen

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  1. 1the [blank_start]normal[blank_end] distribution occurs very [blank_start]often[blank_end] in nature > therefore, is a very important distribution for the statistical analysis of data
    - it is characterised by a symmetrical "[blank_start]bell[blank_end] shape" curve > which corresponds to values near the [blank_start]mean[blank_end] being more common, which values further away from the mean are [blank_start]less[blank_end] common, "tail off" in terms of their frequencies

    1. Anormal
    2. Boften
    3. Cbell
    4. Dmean
    5. Eless
  2. 2in order to understand what it really means for the data to be [blank_start]normally[blank_end] distributed, we first need to consider the idea of probability

    [blank_start]probability[blank_end] = is used to measure the likelihood of an event happening

    if we were to repeat an experiment over and over again, the probability of a particular outcome A is defined as the proportion of the total number of repeats in which A would actually occur, if we were to keep on repeating the experiment we denote this probability by [blank_start]Pr(A)[blank_end]

    example 1: rolling a fair dice
    Let event A be the dice lands with three spots face up; Pr(A) = 1/[blank_start]6[blank_end] = 0.167

    note that in this experiment there are six equally likely outcomes, all with probability of [blank_start]1[blank_end]/6

    note that the probability scale runs between 0 and [blank_start]1[blank_end] inclusive. The higher the number, the [blank_start]more[blank_end] likely the event will be, the sum of the probabilities of all possible events must equal [blank_start]1[blank_end]
    1. Anormally
    2. Bprobability
    3. CPr(A)
    4. D6
    5. E1
    6. F1
    7. Gmore
    8. H1
  3. 3probability example 2: what is probability of a randomly chosen individual having fair hair or blue eyes or both
    - we can estimate the probability of [blank_start]blue[blank_end] eyes by looking at the proportion in a sample with blue eyes
    - we can similarly estimate the probability with [blank_start]fair[blank_end] hair and both fair hair and blue eyes

    TO CALCULATE THIS

    Pr(fair hair or blue eyes or both) = Pr(fair hair) + Pr(blue eyes) [blank_start]-[blank_end] Pr(fair hair AND blue eyes)

    this is an example of the [blank_start]addition[blank_end] rule of probability; the minus sign is to avoid double counting
    1. Ablue
    2. Bfair
    3. C-
    4. Daddition
  4. 4probability example 3: what is the probability of a randomly chosen male having fair hair and being at least 6 foot tall

    - we can estimate the probability by looking at the proportion of males who are at least [blank_start]6[blank_end] foot tall and have fair hair
    - HOWEVER, we can assume that hair colour is unrelated to height then so in this case (BECAUSE THESE 2 VARIABLES/CHARACTERISTICS ARE [blank_start]INDEPENDENT[blank_end], hair colour does not effect height)

    pr(fair hair and height ovr 6ft) = P(fair hair)[blank_start]x[blank_end]Pr(height over 6ft)

    this is called the [blank_start]multiplication[blank_end] rule of probability; this would [blank_start]not[blank_end] work if the two factors are related (not independent)
    1. A6
    2. BINDEPENDENT
    3. Cx
    4. Dmultiplication
    5. Enot
  5. 5probability measurements only really make sense when for discrete outcomes i.e. when we can make a list of [blank_start]all[blank_end] the possible outcomes

    when the measurements are on a [blank_start]continuous[blank_end] scale, such as the length of animals, then there are infinitely many possible outcomes, and it is [blank_start]not[blank_end] possible to list them

    this is where the [blank_start]normal[blank_end] distribution can help us:

    the distributions of lobster lengths have roughly the normal distribution shape for each sex
    1. Aall
    2. Bcontinuous
    3. Cnot
    4. Dnormal
  6. 6[blank_start]Minitab[blank_end] can fit the normal curves for us:

    - suppose we were to take a new measurement for a different female lobster denoted by the outcome X
    > there would be infinite possibilities for the length could be as specific as mm, so it doesn't make sense to ask about the probability of a specific outcome

    instead, meaningful questions will ask if x lies in a particular [blank_start]range[blank_end], e.g. what is the probability that X will be less than 165?
    1. AMinitab
    2. Brange
  7. 7calculating the area under the curve (our particular range of interest)
    - the probability of X lying in any particular range of numbers is given by the [blank_start]area[blank_end] under the curve for the range of interest, the total area under the curve being equal to [blank_start]1[blank_end]

    the [blank_start]normal[blank_end] distribution curve is given by a mathematical formula (image)
    - the distribution is completely determined by 2 parameters, the [blank_start]mean[blank_end] and the standard [blank_start]deviation[blank_end]

    this means it is possible to calculate areas under the curve, and hence probabilities
    - fortunately minitab can do this for us
    1. Aarea
    2. B1
    3. Cnormal
    4. Dmean
    5. Edeviation
  8. 8the [blank_start]normal[blank_end] distribution is useful for it is then used to model our data, and makes it easy to calculate the probability of an outcome in any given range (i.e. below/above a value)
    - can only do this because we our modelling with a normal distribution
    - the normal distribution acts as a model for the way data behaves
    1. Anormal
  9. 9An important property of the normal distribution is that [blank_start]95[blank_end]% of our data is going to lie within [blank_start]1.96[blank_end] (we say 2) standard deviations of the mean

    similarly, [blank_start]two[blank_end]-thirds of the data lies within 1 standard [blank_start]deviation[blank_end] of the mean and virtually all the data lies within [blank_start]3[blank_end] standard deviations of the mean
    1. A95
    2. B1.96
    3. Ctwo
    4. Ddeviation
    5. E3
  10. 10The distribution of the sample mean

    - looking at IQ, it is measured on a scale which is designed so that population distribution is normal, with mean [blank_start]100[blank_end] and standard deviation 15
    1. A100

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Stats Quiz am The normal distribution, erstellt von sophie waddington am 24/12/2018.
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