Solved: If Z is N(0, 1), find

Chapter 3, Problem 1E

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QUESTION:

If \(Z\) is \(N(0,1)\), find

(a) \(P(0.53<Z \leq 2.06)\).

(b) \(P(-0.79 \leq Z<1.52)\).

(c) \(P(Z>-1.77)\).

(d) \(P(Z>2.89)\).

(e) \(P(|Z|<1.96)\).

(f) \(P(|Z|<1)\).

(g) \(P(|Z|<2)\).

(h) \(P(|Z|<3)\).

Equation Transcription:




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Text Transcription:

Z

N(0,1)

P(0.53<Z < or = 2.06)

P(−0.79 < or = Z<1.52)  

P(Z>−1.77)

P(Z>2.89)

P(|Z|<1.96)

P(|Z|<1)

P(|Z|<2)

P(|Z|<3

Questions & Answers

QUESTION:

If \(Z\) is \(N(0,1)\), find

(a) \(P(0.53<Z \leq 2.06)\).

(b) \(P(-0.79 \leq Z<1.52)\).

(c) \(P(Z>-1.77)\).

(d) \(P(Z>2.89)\).

(e) \(P(|Z|<1.96)\).

(f) \(P(|Z|<1)\).

(g) \(P(|Z|<2)\).

(h) \(P(|Z|<3)\).

Equation Transcription:




.

.

.

.

.

Text Transcription:

Z

N(0,1)

P(0.53<Z < or = 2.06)

P(−0.79 < or = Z<1.52)  

P(Z>−1.77)

P(Z>2.89)

P(|Z|<1.96)

P(|Z|<1)

P(|Z|<2)

P(|Z|<3

ANSWER:

Solution :

Step 1 of 3:

If Z is the standard normal distribution  N(0,1). We have to find the probabilities.

  1. P(0.53<Z2.06)
  2. P(-0.79Z<1.52)
  3. P(Z>-1.77)
  4. P(Z>2.89)
  5. P(|Z| >1.96)
  6. P(|Z|<1)
  7. P(|Z|<2)
  8. P((|Z|<3).

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