b PX77 When X77 07PX77 Pz07 1 07580 0242 cP60X75 When X60 z 60 7010 1

# B px77 when x77 07px77 pz07 1 07580 0242 cp60x75 when

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b. P(X≥77) = ? When X=77, z = 77 70 10 = 0.7 P(X≥77) = P(z≥0.7) = 1-0.7580 = 0.242 c. P(60≤X≤75) = ? When X=60, z = 60 70 10 =− 1 When X=75, z = 75 70 10 = 0.5 P(60≤X≤75) = P(-1≤z≤0.5) = P(z≤0.5) - P(z≤-1) = 0.6915 – 0.1587 = 0.5328 d. Probability of 0.95 on the lower tail corresponds to z =1.645 1.645 = x 70 10 x = 1.645 × 10 + 70
x = 86.45 3.) Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways. a. Compute the probability of receiving three calls in a 5-minute interval of time. b. Compute the probability of receiving exactly 10 calls in 15 minutes. c. Compute the probability of receiving at most 3 calls in 5 minutes. 3.) a. µ = 48/12 = 4, x = 3 f (3) = 4 3 e 4 3 ! = 0.195 b . µ = 48/4 = 12, x = 10 f (3) = 12 10 e 12 10 ! = 0.105 c. µ = 48/12 = 4, x = 3, 2, 1, 0 f (at most 3) = f(0) + f(1) + f(2) + f(3) = 4 0 e 4 0 ! + 4 1 e 4 1 ! + 4 2 e 4 2 ! + 4 3 e 4 3 ! = 0.018 + 0.073 + 0.147 + 0.195 = 0.434 Standard Deviation STAT – Edit – enter numbers – STAT CALC – 1-vars stats Binomial Probabilities (Binomial pdf) P(x=C) = binom pdf (n,p,c) n = # of trials 2 nd VARS – binom pdf – enter data p = prob. Of success x-value Probability Distribution (random variables) 2 nd VARS Normal pdf (probability density function) -used to find a single value of the random variable x. Normal cdf (cumulative distribution function) -used to find the cumulative probability from zero up to the same input value of random variable x. InvNorm -used to find the x-value given the probability region is to the left of the x-value. A sample statistic is a piece of statistical information you get from a handful of items. A discrete variable is a variable which can only take a countable number of values. In this example, the number of heads can only take 4 values (0, 1, 2, 3) and so the variable is discrete . The variable is said to be random if the sum of the probabilities is one. The combination rule is a special application of the partition rule

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• Summer '18
• David Grimmett
• Normal Distribution, Probability theory, Cumulative distribution function

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