Question

(1 point) For each probability expression, find the unknown ?z-value(s). Unless directed otherwise, use three decimals in your answers.

(a) ?(?≤?0)=0.87 Find ?0

?0=

(b) ?(?≤?0)=0.17 Find ?0

?0=

(c) ?(?≥?0)=0.3 Find ?0

?0=

(c) ?(?0≤?≤0.11)=0.4717P Find ?0

?0

(use two decimals)

Answer 1

SOLUTION:

From given data,

(1 point) For each probability expression, find the unknown z-value(s). Unless directed otherwise, use three decimals in your answers.

(a) ?(? ≤ ?₀) = 0.87 Find ?0

?(? ≤ ?₀) = 0.87

The z-score is,

From the standard normal table,the indicated z score for the area of 0.87 and indicative area 0.87 is 1.126 then

?(? ≤ 1.126 ) = 0.87

Where, ?₀ = 1.126 (Rounded to three decimal places)

(b) ?(?≤ ?₀) = 0.17 Find ?₀

?(?≤ ?₀) = 0.17

The z-score is,

From the standard normal table,the indicated z score for the area of 0.17 and indicative area 0.17 is 0.954 then

?(? ≤ 0.954 ) = 0.17

Where, ?₀ = 0.954 (Rounded to three decimal places)

(c) ?(? ≥ ?₀) = 0.3 Find ?₀

?(? ≥ ?₀) = 0.3

1 - ?(? < ?₀) = 0.3

?(? < ?₀) = 1 - 0.3

?(? < ?₀) = 0.7

The z-score is,

From the standard normal table,the indicated z score for the area of 0.3 subtract from 1 and indicative area 0.7 is 0.524 then

?(? < 0.524 ) = 0.7
Where, ?₀ = 0.524 (Rounded to three decimal places)

(d) ?(?₀  ≤ ? ≤ 0.11) = 0.4717 Find ?₀

?(?₀  ≤ ? ≤ 0.11) = ?(? ≤ ?₀) - ?(? ≤ 0.11)

?(? ≤ ?₀) - ?(? ≤ 0.11) = 0.4717

  ?(? ≤ ?₀) =  0.4717-?(? ≤ 0.11)

     ?(? ≤ ?₀) = 0.4717 - 0.4562

?(? ≤ -2.157) = 0.0155

Where, ?₀ = -2.157 (Rounded to three decimal places)

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