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Chapter 6: Q 55 (page 387)

X~N(鈥�3,4)

Find the probability that x is between one and four.

Short Answer

Expert verified

The value of P(1<x<4)is0.1186.

Step by step solution

01

Given Information

Given that,

X~N(-3,4)

Where,

渭=-3and

蟽=4

02

Explanation

Now, the required probability can be calculated as below:

P(1<x<4)=P(x<4)-P(x<1)

=P(x-渭蟽<4-渭蟽)-P(x-渭蟽<1-渭蟽)

=P(Z<4-(-3)4)-P(Z<1-(-3)4)

=P(Z<74)-P(Z<44)

=P(Z<1.75)-P(Z<1)

=0.9599-0.8413{From standardnormal table}

=0.1186

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Most popular questions from this chapter

Suppose X ~ N(4, 2). What value of x is 1.5 standard deviations to the left of the mean?

Define the random variable X in words. X = _______________.

A bottle of water contains 12.05fluid ounces with a standard deviation of 0.01ounces. Define the random variable Xin words. X=____________.

Suppose a normal distribution has a mean of six and a standard deviation of 1.5. What is the z-score of x = 5.5?

X~N(-2,1)渭=_____________
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