Question

In: Statistics and Probability

A population is normally distributed with muμequals=100100 and sigmaσequals=2525. a. nbspa. Find the probability that a...

A population is normally distributed with

muμequals=100100

and

sigmaσequals=2525.

a. nbspa.

Find the probability that a value randomly selected from this population will have a value greater than

115115.

b.

Find the probability that a value randomly selected from this population will have a value less than

9090.

c.

Find the probability that a value randomly selected from this population will have a value between

9090

and

115115.

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Click the icon to view the standard normal table.

a. P(xgreater than>115115)equals=

(Round to four decimal places as needed.)b. P(xless than<9090)equals=

(Round to four decimal places as needed.)c. P(9090less than<xless than<115115)equals=

(Round to four decimal places as needed.)

Expert Solution

Answer: A population is normally distributed with

μ =100 and

σ = 25.

a) Find the probability that a value randomly selected from this population will have a value greater than 115.

P(X > 115) = P(x - μ/σ > 115 - 100 / 25)

P(X > 115) = P(Z > 0.60)

P(X > 115) = 0.2743

Therefore, the probability that a value randomly selected from this population have a value greater than 115 would be 0.2743.

b) Find the probability that a value randomly selected from this population will have a value less than 90.

P(X < 90) = P(x - μ/σ < 90 - 100 / 25)

P(X < 90) = P(Z < - 0.40)

P(X < 90) = 0.3446

Therefore, the probability that a value randomly selected from this population have a value less than 115 would be 0.3446.

c) Find the probability that a value randomly selected from this population will have a value between 90 and 115.

P(90 X < 115) = P(90 - 100 /25 < Z < 115 - 100 /25)

P(90 X < 115) = P(- 0.40 < Z < 0.60)

P(90 X < 115) = P(Z< 0.60) - P(Z< -0.40)

P(90 X < 115) = 0.7258 - 0.3446

P(90 X < 115) = 0.3812

Therefore, the probability that a value randomly selected from this population have a value between 90 and 115 would be 0.3812.

orchestra answered 2 years ago

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