Answered: 1 A random variable, x, has a standard…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A random variable, x, has a standard normal distribution. Calculate the probability that x lies in the following intervals: (a) (0.25,0.75) ® (~03.0.1) (c) within 1.5 standard deviations of the mean (d) more than two standard deviations from the mean (@ (~1.7.-02) A random variable, x, has a normal distribution with ‘mean 4 and standard deviation 0.8. Calculate the probability that @ 3046 @ x0 © 16 The scores from IQ tests have a mean of 100 and a standard deviation of 15. What should a person score in order to be described as in the top 10% of the population? A machine produces car pistons. The diameter of the pistons follows a normal distribution, mean 6.04 cm with a standard deviation of 0.02 cm. The piston is acceptable if its diameter is in the range 6.010 cm to 6.055 cm. What percentage of pistons is acceptable? 1€ The random variable, x. has a normal distribution. How many standard deviations above the mean must the point P be placed if the tail-end is to represent @ 10% (b) 5% () 1% of the total area? (See Figure 29.20.) Nx) Figure 29.20 Graph for Question 6. Consider Figure 29.21. The two tail-ends have equal area. How many standard deviations from the mean must A and B be placed if the tail-ends are (a) 10% (b) 5% () 1% of the total area? Nx) Figure 29.21 Graph for Question 7. . (a) 0.1747 (b) 0.1577 (c) 0.8664 (d) 0.0455 (e) 03762 . (a) 0.5858 (b) 0.4199 (c) 0.2266 (d) 0.5987 (e) 0.5467 3 @ 04436 () 06554 () 02604 (d) 05544 & 1 & n% & @128 ® 1685 7 @ies ®196 (©233 (©2.57

EXERCISES 29.14
A random variable, x, has a standard normal
distribution. Calculate the probability that x lies in the
following intervals:
The random variable, x, has a normal distribution.
How many standard deviations above the mean must
the point P be placed if the tail-end is to represent
(a) (0.25, 0.75)
(a) 10%
(b) 5%
(c) 1%
(b) (-0.3, 0.1)
of the total area? (See Figure 29.20.)
(c) within 1.5 standard deviations of the mean
(d) more than two standard deviations from the mean
N(x) A
(e) (-1.7, -0.2)
A random variable, x, has a normal distribution with
mean 4 and standard deviation 0.8. Calculate the
probability that
(a) 3.0 <x< 4.4
(b) 2.5 <x < 3.9
Figure 29.20
Graph for Question 6.
(c) x> 4.6
(d) x< 4.2
(e) x is within 0.6 of the mean
Consider Figure 29.21. The two tail-ends have equal
area. How many standard deviations from the
must A and B be placed if the tail-ends are
A random variable, t, has a normal distribution with
ean
mean 1 and standard deviation 2.5. Calculate the
probability that
(a) -1 <1<2
(a) 10%
(b) 5%
(c) 1%
(b) t >0
of the total area?
(c) t| < 0.9
(d) t| > 1.6
The scores from IQ tests have a mean of 100 and a
standard deviation of 15. What should a person score
in order to be described as in the top 10% of the
population?
N(x) A
5 A machine produces car pistons. The diameter of the
pistons follows a normal distribution, mean 6.04 cm
with a standard deviation of 0.02 cm. The piston is
acceptable if its diameter is in the range 6.010 cm to
6.055 cm. What percentage of pistons is
ассeptable?
A
B
Figure 29.21
Graph for Question 7.
Solutions
(a) 0.1747
(d) 0.0455
(b) 0.1577
(c) 0.8664
119
(e) 0.3762
71%
2 (a) 0.5858
(d) 0.5987
(b) 0.4199
(c) 0.2266
(e) 0.5467
6 (a) 1.28
(b) 1.645
(c) 2.33
3 (a) 0.4436
(b) 0.6554
(c) 0.2604
7 (a) 1.64
(b) 1.96
(c) 2.57
(d) 0.5544

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1 A random variable, x, has a standard normal distribution. Calculate the probability that x lies in the following intervals: (a) (0.25, 0.75) (b) (-0.3, 0.1) (c) within 1.5 standard deviations of the mean (d) more than two standard deviations from the mean (e) (-1.7, –0.2)