Chapter 4: Q88E (page 262)

Find a value of the standard normal random variable z, call it $z_{0}$ such that
$a . P (- z_{0} \leq z \leq z_{0}) = . 98 b . P (z \geq z_{0}) = . 05 c . P (z \geq z_{0}) = . 70 d . P (z \geq z_{0}) = . 025 e . P (z \leq z_{0}) = . 70$

Short Answer

Expert verified

$a . z_{0} = 2.326 b . z_{0} = 1.645 c . z_{0} = - 0.524 d . z_{0} = 1.96 e . z_{0} = 0.524$

Step by step solution

Given information

z is a standard normal variable, which is called $z_{0}$ .

Finding the value of z0 when P(-z0≤z≤z0)=.98

$a . P (- z_{0} \leq z \leq z_{0}) = 0.98 2 P (0 \leq z \leq z_{0}) = 0.98 [D u e t o s y m m e t r i c d i s t r u b u t i o n] P (0 \leq z \leq z_{0}) = 0.49 P (z \leq z_{0}) - P (z < 0) = 0.49 P (z \leq z_{0}) - 0.50 = 0.49 P (z \leq z_{0}) = 0.99 Φ (z_{0}) = 0.99 z_{0} = Φ^{- 1} (0.99) z_{0} = 2.326$

Therefore, the z₀the score is 2.326.

Finding the value of z0 when P(z≥z0)=.05

$P (z \geq z_{0}) = 0.05 1 - P (z < z_{0}) = 0.05 P (z < z_{0}) = 0.95 Φ (z_{0}) = 0.95 z_{0} = Φ^{- 1} (0.95) z_{0} = 1.645$

Therefore, the z₀ score is 1.645.

Finding the value of z0 when P(z≥z0)=.70

$P (z \geq z_{0}) = 0.70 1 - P (z \geq z_{0}) = 0.70 P (z \geq z_{0}) = 0.30$

Therefore, the score is -0.524.

Finding the value of z0 when P(z≥z0)=.70

$d . P (z \geq z_{0}) = 0.025 1 - P (z < z_{0}) = 0.025 P (z < z_{0}) = 0.975 Φ (z_{0}) = 0.975 z_{0} = Φ^{- 1} (0.975) z_{0} = 1.96$

Therefore, the z₀ score is 1.96.

Finding the value z0 of when P(z≤z0)=.70

$e . P (z \leq z_{0}) = 0.70 Φ (z_{0}) = 0.70 z_{0} = Φ^{- 1} (0.70) z_{0} = 0.524$

Therefore, the z₀ score is 0.524.

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Find a value of the standard normal random variable z, call it $z_{0}$ such that
$a . P (- z_{0} \leq z \leq z_{0}) = . 98 b . P (z \geq z_{0}) = . 05 c . P (z \geq z_{0}) = . 70 d . P (z \geq z_{0}) = . 025 e . P (z \leq z_{0}) = . 70$

Short Answer

Step by step solution

Given information

Finding the value of z0 when P(-z0≤z≤z0)=.98

Finding the value of z0 when P(z≥z0)=.05

Finding the value of z0 when P(z≥z0)=.70

Finding the value of z0 when P(z≥z0)=.70

Finding the value z0 of when P(z≤z0)=.70

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Find a value of the standard normal random variable z, call itz0 such thata.P(-z0≤z≤z0)=.98b.P(z≥z0)=.05c.P(z≥z0)=.70d.P(z≥z0)=.025e.P(z≤z0)=.70

Short Answer

Step by step solution

Given information

Finding the value of z0 when P(-z0≤z≤z0)=.98

Finding the value of z0 when P(z≥z0)=.05

Finding the value of z0 when P(z≥z0)=.70

Finding the value of z0 when P(z≥z0)=.70

Finding the value z0 of when P(z≤z0)=.70

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Decision Maths

Mechanics Maths

Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Find a value of the standard normal random variable z, call it $z_{0}$ such that
$a . P (- z_{0} \leq z \leq z_{0}) = . 98 b . P (z \geq z_{0}) = . 05 c . P (z \geq z_{0}) = . 70 d . P (z \geq z_{0}) = . 025 e . P (z \leq z_{0}) = . 70$