Question

V. Simple and joint events Following are success data for businesses in one city. Not profitable Profitable 23 29 Company size Large Medium Small Total 59 14 Total 52 73 212 337 180 262 32 75 A company is randomly selected. Which of these outcomes are simple events and which are joint events? Large but not profitable • Medium sized Small sized • Profitable and small size

Answer 1

V) Simple events are:

Medium sized

Small sized

Joint events are:

Large but not profitable

Profitable and small size

A) P(medium size) = 73/337 = 0.2166

B) P(small sized and profitable) = 180/337 = 0.5341

C) P(large sized or not profitable) = (52 + 75 - 29)/337 = 98/337 = 0.2908

D) P(not profitable | medium sized) = 14/73 = 0.1918

IX) $\pi$ = 0.85

     n = 11

It is a binomial distribution.

P(X = x) = nCx * p^x *I (1 - p)^{n - x}

P(X > 9) = P(X = 9) + P(X = 10) + P(X = 11)

              = 11C9 * (0.85)^9 * (0.15)^2 + 11C10 * (0.85)^10 * (0.15)^1 + 11C11 * (0.85)^11 * (0.15)^0

              = 0.7788

X) n = 25

    p = 0.66

P(X = 16) = 25C16 * (0.66)^16 * (0.34)^9 = 0.1608

XI) Expected number = 2/7 * 50 = 14.2857 = 14

XII) P(1.13 < Z < 2.08)

= P(Z < 2.08) - P(Z < 1.13)

= 0.9812 - 0.8708

= 0.1104

XIII) P(Z > Z₀) = 0.0725

or, 1 - P(Z < Z₀) = 0.0725

or, P(Z < Z₀) = 0.9275

or, Z₀ = 1.46

XIV) P(80 < X < 95)

= P((80 - $\mu$)/$\sigma$ < (X - $\mu$)/$\sigma$ < (95 - $\mu$)/$\sigma$)

= P((80 - 83)/7.2 < Z < (95 - 83)/7.2)

= P(-0.42 < Z < 1.67)

= P(Z < 1.67) - P(Z < -0.42)

= 0.9525 - 0.3372

= 0.6153

XV) P(5.3 < X < 10.5)

= P((5.3 - $\mu$)/$\sigma$ < (X - $\mu$)/$\sigma$ < (10.5 - $\mu$)/$\sigma$)

= P((5.3 - 6.8)/3.8 < Z < (10.5 - 6.8)/3.8)

= P(-0.39 < Z < 0.97)

= P(Z < 0.97) - P(Z < -0.39)

= 0.8340 - 0.3483

= 0.4857

XVI) P(X > x) = 0.2

or, P((X - $\mu$)/$\sigma$ > (x - $\mu$)/$\sigma$) = 0.2

or, P(Z > (x - 102155)/6450) = 0.2

or, P(Z < (x - 102155)/6450) = 0.8

or, (x - 102155)/6450 = 0.84

or, x = 0.84 * 6450 + 102155

or, x = 107573