For this week’s homework, we will revisit some old homework problems. But this time we’ll use R to solve them (you must use R to do problems

Question

For this week’s homework, we will revisit some old homework problems. But this time we’ll use R to solve them (you must use R to do problems 1 – 5). We’ll also collect a little data in class. 1) Find the following probabilities: a) Pr{Z < 4.3} b) Pr{Z > -1.69} c) Pr{-1.12 < Z < 1.12} d) Pr{-1.3 < Z < 0.98} e) Pr{Z < -1.12 or Z > 1.12} (you want the probability outside the range -2.67 to 2.67)

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Thiên Thanh 3 years 2021-09-04T15:31:40+00:00 1 Answers 4 views 0

Answers ( )

  1. minhkhue
    0
    2021-09-04T15:32:50+00:00
    Reply

    Answer:

    P(Z < 4.3) = 0.9999

    P(Z> -1.69) = 0.9545

    P(-1.12 < Z < 1.12) = 0.7373

    P(-1.3 < Z < 0.98) = 0.7397

    P(Z < -1.12\ or\ Z > 1.12) = 0.2628

    Step-by-step explanation:

    To answer these questions, we will make use of a z score table

    Solving (a): P(Z < 4.3)

    P(Z < 4.3) = 0.9999

    Solving (b): P(Z> -1.69)

    First, we rewrite this using complement rule

    P(Z> -1.69) = 1 - P(Z < -1.69)

    From the z score table:

    P(Z< -1.69) = 0.045514

    So, we have:

    P(Z> -1.69) = 1 - 0.045514

    P(Z> -1.69) = 0.9545

    Solving (c) P(-1.12 < Z < 1.12)

    This is equivalent to:

    P(-1.12 < Z < 1.12) = P(Z<1.12) - P(Z<-1.12)

    Use the z score table

    P(-1.12 < Z < 1.12) = 0.86864 - 0.13136

    P(-1.12 < Z < 1.12) = 0.7373

    Solving (d) P(-1.3 < Z < 0.98)

    This is equivalent to

    P(-1.3 < Z < 0.98) = P(Z<0.98)- P(Z<-1.3)

    P(-1.3 < Z < 0.98) = 0.83646- 0.0968

    P(-1.3 < Z < 0.98) = 0.7397

    Solving (e) P(Z < -1.12 or Z > 1.12)

    This is interpreted as:

    P(Z < -1.12\ or\ Z > 1.12) = P(Z < -1.12) + P(Z > 1.12)

    Apply complement rule

    P(Z < -1.12\ or\ Z > 1.12) = P(Z < -1.12) + 1 - P(Z < 1.12)

    P(Z < -1.12\ or\ Z > 1.12) = 0.1314 + 1 - 0.8686

    P(Z < -1.12\ or\ Z > 1.12) = 0.2628

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