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Chapter 6: Q.6.71 (page 390)

The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of five minutes and a standard deviation of two minutes.

Find the probability that it takes at least eight minutes to find a parking space.

a. 0.0001

b. 0.9270

c. 0.1862

d. 0.0668

Short Answer

Expert verified

The probability that it takes at least eight minutes to find a parking space0.0668that is option d.

Step by step solution

01

Step: Given information

Given in the question that

Mean=5

Standard deviation=2

02

Solution

Here,

μ=5

σ=2

So, the required probability calculation is given below,

P(x≥8)=1−P(x<8)

=1−Px−μσ<8−μσ

=1−PZ<8−52

=1−P(Z<1.5)

=1−0.9332From standardnormal table

=0.0668

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Most popular questions from this chapter

The life of Sunshine CD players is normally distributed with a mean of 4.1years and a standard deviation of 1.3years. A CD player is guaranteed for three years. We are interested in the length of time a CD player lasts. Find the probability that a CD player will break down during the guarantee period.

a. Sketch the situation. Label and scale the axes. Shade the region corresponding to the probability.

b. P(0<x<____________)=___________(Use zero for the minimum value of x.)

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet.

a. If X=distance in feet is for a fly ball, then X~

b. If one fly ball is randomly chosen from this distribution, what is the probability that this ball will travel fewer than 220 feet? Sketch the graph. Scale the horizontal axis XShade the region corresponding to the probability. Find the probability.

c. Find the 80ithpercentile of the distribution of fly balls. Sketch the graph, and write the probability statement.

A The distance of fly balls hit to the outfield in baseball is denoted as: N~N(250,50)

B: The probability that a randomly selected fly ball traveled fewer than 220 feet is given by P(x<220)=0.2743

Use the information in Example 6.10 to answer the following questions.

  1. Find the 30thpercentile, and interpret it in a complete sentence.
  2. What is the probability that the age of a randomly selected smartphone user in the range 13to 55+is less than 27years old.

How would you represent the area to the left of one in a probability statement?

About what percent of xvalues lie between the second and third standard deviations (both sides)?
See all solutions

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