Question

# A: Let z be a random variable with a standard normal distribution. Find the indicated probability....

A: Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)
P(z ≤ 1.11) =

B: Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)

P(z ≥ −1.24) =

C: Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)

P(−1.78 ≤ z ≤ −1.14) =

D: Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

μ = 40; σ = 16

P(50 ≤ x ≤ 70) =

E: Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

μ = 97; σ = 12

P(x ≥ 90) =

We need to use standard normal z table to solve this problem

A)

From z table, P(z<1.11) = 0.8665

B)

From z table, P(z>-1.24) = 0.8925

C)

P(-1.78<z<-1.14) = p(z<-1.14) - p(z<-1.78)

P(z<-1.14) = 0.1271

P(z<-1.78) = 0.0375

So answer is 0.1271 - 0.0375 = 0.0896

D)

As the data is normally distributed we can use standard normal z table to estimate the answers

Z = (x-mean)/s.d

Given mean = 40

S.d = 16

P(50 < x< 70)

P(x<70)

Z = (70-40)/16 = 1.88

From z table, P(z<1.88) = 0.9699

P(x<50)

Z = (50 - 40)/16 = 0.63

From z table, P(z<0.63) = 0.7357

Required probability is 0.9699 - 0.7357 = 0.2342

E)

P(x>90)

Z = (90 - 97)/12 = -0.58

From.z.table, P(z>-0.58) = 0.7190

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The text contains multiple questions related to finding probabilities for standard normal distributions and normal distributions with given means and standard deviations. Answers to each of these questions are provided, using z-tables and standard normal distribution properties.
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Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
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- MULTIPLE_QUESTIONS
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Question

# A: Let z be a random variable with a standard normal distribution. Find the indicated probability....

A: Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)
P(z ≤ 1.11) =

B: Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)

P(z ≥ −1.24) =

C: Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)

P(−1.78 ≤ z ≤ −1.14) =

D: Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

μ = 40; σ = 16

P(50 ≤ x ≤ 70) =

E: Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

μ = 97; σ = 12

P(x ≥ 90) =

We need to use standard normal z table to solve this problem

A)

From z table, P(z<1.11) = 0.8665

B)

From z table, P(z>-1.24) = 0.8925

C)

P(-1.78<z<-1.14) = p(z<-1.14) - p(z<-1.78)

P(z<-1.14) = 0.1271

P(z<-1.78) = 0.0375

So answer is 0.1271 - 0.0375 = 0.0896

D)

As the data is normally distributed we can use standard normal z table to estimate the answers

Z = (x-mean)/s.d

Given mean = 40

S.d = 16

P(50 < x< 70)

P(x<70)

Z = (70-40)/16 = 1.88

From z table, P(z<1.88) = 0.9699

P(x<50)

Z = (50 - 40)/16 = 0.63

From z table, P(z<0.63) = 0.7357

Required probability is 0.9699 - 0.7357 = 0.2342

E)

P(x>90)

Z = (90 - 97)/12 = -0.58

From.z.table, P(z>-0.58) = 0.7190

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Coins can be redeemed for fabulous gifts.
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The text contains multiple questions related to finding probabilities for standard normal distributions and normal distributions with given means and standard deviations. Answers to each of these questions are provided, using z-tables and standard normal distribution properties.

TYPE: MULTIPLE_QUESTIONS_WITH_ANSWERS