Question

In: Math

1.Given the following sampling distribution: X -18 -13 -2 10 19 P(X) 1⁄25 9⁄100 7⁄100 2⁄25...

1.Given the following sampling distribution:

X	-18	-13	-2	10	19
P(X)	¹⁄₂₅	⁹⁄₁₀₀	⁷⁄₁₀₀	²⁄₂₅	___

What is P(X = 19)

2. Given the following sampling distribution:

X	-20	-11	-7	12	14
P(X)	¹⁄₂₅	³⁄₁₀₀	⁹⁄₁₀₀	¹⁄₅₀	___

What is P(X > -11)?

3.Given the following sampling distribution:

X	-19	-14	-3	5	15
P(X)	¹⁄₂₅	⁹⁄₁₀₀	⁷⁄₁₀₀	²⁄₂₅	___

What is the mean of this sampling distribution?

Solutions

Expert Solution

Q.1) P(X = 19) = 1 - [(1/25) + (9/100) + (7/100) + (2/25)]

=> P(X = 19) = 1 - [(4/100) + (9/100) + (7/100) + (8/100)]

=> P(X = 19) = 1 - [(4+9+7+8)/100]

=> P(X = 19) = 1 - (28/100)

=> P(X = 19) = 72/100

=> P(X = 19) = 18/25

=> P(X = 19) = 0.72

Q.2) P(X = 14) = 1 - [(1/25) + (3/100) + (9/100) + (1/50)]

=> P(X = 14) = 1 - [(4/100) + (3/100) + (9/100) + (2/100)]

=> P(X = 14) = 1 - [(4+3+9+2)/100]

=> P(X = 14) = 1 - (18/00)

=> P(X = 14) = 82/100

=> P(X = 14) = 0.82

Therefore,

P(X > -11) = P(X = -7) + P(X = 12) + P(X = 14)

=> P(X > -11) = 9/100 + 1/50 + 82/100

=> P(X > -11) = (9/100) + (2/100) + (82/100)

=> P(X > -11) = (9 + 2 + 82) / 100

=> P(X > -11) = 93/100

=> P(X > -11) = 0.93

Q.3) P(X = 15) = 1 - [(1/25) + (9/100) + (7/100) + (2/25)]

=> P(X = 15) = 1 - [(4/100) + (9/100) + (7/100) + (8/100)]

=> P(X = 15) = 1 - [(4+9+7+8)/100]

=> P(X = 15) = 1 - (28/100)

=> P(X = 15) = 72/100

=> P(X = 15) = 18/25

Expected value of X is,

E(X) = [ (-19 * 1/25) + (-14 * 9/100) + (-3 * 7/100) + (5 * 2/25) + (15 * 18/25) ]

=> E(X) = -0.76 - 1.26 - 0.21 + 0.4 + 10.8

=> E(X) = 8.97

Therefore, mean of this sampling distribution is 8.97

milcah answered 8 months ago

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