Edexcel A Level Maths - Year 2 Statistics

what is the logarithmic equation/derivation for y = axⁿ ? (polynomial)

log y = log a + n log x

what is the logarithmic equation/derivation for y = an^x ? (exponential)

log y = log a + x log n

what is the product moment correlation coefficient r ?

• measurement of relationship between two variables - takes value between - 1 and 1

• 1 - perfect positive linear correlation

• -1 - perfect negative linear correlation

• 0 - no linear correlation

what probability rules occur for independent events?

• P (A|B) = P(A|B’) = P(A)

• P(B|A) = P(B|A’) = P(B)

what does P (A U B) = ?

P(A) + P(B) - P( A n B)

P(B n A) =

P(B|A) x P(A)

what does the area under a normal distribution curve equal?

1

what are some characteristics of a normal distribution?

• has parameteres u and o², mean and variance

• is symmetrical so mean = median = mode

• bell shaped curve with asymptotes at each end

• has points of inflection at u + o and u - o

what percentage of data lies within 1 sd of the mean in a normal distribution?

68%

what percentage of data lies within 2 sd of the mean in a normal distribution?

95%

what percentage of data lies within 3 sd of the mean in a normal distribution?

99.7%

what is the standard normal distribution?

Z ~ N(0,1²)

how would you convert (code) a normal distribution to the standard normal distribution?

Z = (X- u)/o

what are the conditions for a normal approximation to the binomial distribution?

• n is large

• p is close to 0.5

how would you approximate the binomial distribution with the normal?

• u = np

• o = rt (np(1-p))

• apply a continuity correction (X~B, Y~N)

  • if X>5 → Y>5.5

  • if X>= 5 → Y>4.5

  • if X = 5, 4.5 < Y < 5.5

  • if X < 5, Y < 4.5

  • if X <= 5, Y < 5.5

if a sample of size n is taken from a normally distributed random variable, what is the sample mean distribution?

• X bar ~ N(u, o²/n)

• can be coded to normal where Z = (X bar - u)/ (o²/n)