Question

The Rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal and then measuring the depth of penetration of the point. Suppose the Rockwell hardness of a particular alloy is normally distributed with mean 69 and standard deviation 3.

(a) If a specimen is acceptable only if its hardness is between
64 and 73, what is the probability that a randomly chosen specimen
has an acceptable hardness? (Round your answer to four decimal
places.)

(b) If the acceptable range of hardness is (69 − *c*, 69 +
*c*), for what value of *c* would 95% of all
specimens have acceptable hardness? (Round your answer to two
decimal places.)

(c) If the acceptable range is as in part (a) and the hardness of
each of ten randomly selected specimens is independently
determined, what is the expected number of acceptable specimens
among the ten? (Round your answer to two decimal places.)

specimens

(d) What is the probability that at most eight of ten independently
selected specimens have a hardness of less than 71.52?
[*Hint*: *Y* = the number among the ten specimens
with hardness less than 71.52 is a binomial variable; what is
*p*?] (Round your answer to four decimal places.)

Answer #1

a)

for normal distribution z score =(X-μ)/σx | |

here mean= μ= | 69 |

std deviation =σ= | 3.000 |

probability
=P(64<X<73)=P((64-69)/3)<Z<(73-69)/3)=P(-1.67<Z<1.33)=0.9082-0.0475=0.8607 |

b)

since for middle 95% values, z =1.96

c =z*std deviation =3*1.96 =**5.88**

c)

expected number of acceptable specimens among the ten
=np=10*0.8607 =**8.61**

d)

probability =P(X<71.52)=(Z<(71.52-69)/3)=P(Z<0.84)=0.7995 |

probability that at most eight of ten independently selected specimens have a hardness of less than 71.52:

P(X<=8)= |
∑_{x=0}^{a }
(_{n}C_{x})p^{x}(1−p)^{(n-x) }
= |
0.6257 |

The Rockwell hardness of a metal is determined by impressing a
hardened point into the surface of the metal and then measuring the
depth of penetration of the point. Suppose the Rockwell hardness of
a particular alloy is normally distributed with mean 69 and
standard deviation 3.
(a) If a specimen is acceptable only if its hardness is between
68 and 76, what is the probability that a randomly chosen specimen
has an acceptable hardness? (Round your answer to four...

The Rockwell hardness of a metal is determined by impressing a
hardened point into the surface of the metal and then measuring the
depth of penetration of the point. Suppose the Rockwell hardness of
a particular alloy is normally distributed with mean 69 and
standard deviation 3.
(a) If a specimen is acceptable only if its hardness is between
67 and 73, what is the probability that a randomly chosen specimen
has an acceptable hardness? (Round your answer to four...

The Rockwell hardness of a metal is determined by impressing a
hardened point into the surface of the metal and then measuring the
depth of penetration of the point. Suppose the Rockwell hardness of
a particular alloy is normally distributed with mean 69 and
standard deviation 3.
(a) If a specimen is acceptable only if its hardness is between
64 and 74, what is the probability that a randomly chosen specimen
has an acceptable hardness? (Round your answer to four...

The Rockwell hardness of a metal is determined by impressing a
hardened point into the surface of the metal and then measuring the
depth of penetration of the point. Suppose the Rockwell hardness of
a particular alloy is normally distributed with mean 69 and
standard deviation 3. (Rockwell hardness is measured on a
continuous scale.)
(a) If a specimen is acceptable only if its hardness is between
67 and 75, what is the probability that a randomly chosen specimen
has...

Part 1
The Rockwell hardness of a metal is determined by impressing a
hardened point into the surface of the metal and then measuring the
depth of penetration of the point. Suppose the Rockwell hardness of
a particular alloy is normally distributed with mean 72 and
standard deviation 3.
(b) If the acceptable range of hardness is (72 − c, 72
+ c), for what value of c would 95% of all
specimens have acceptable hardness? (Round your answer to...

The hardness of a metal is determined by forcing a hardened
point into the surface and then measuring the depth of penetration
of the point. Suppose the hardness of a particular metal is
normally distributed with mean 70 and standard deviation 3.
If a sample is acceptable only if its hardness is between 67
and 75, what is the probability that a randomly chosen sample has
an acceptable hardness? (12 pts)
If the acceptable range of hardness is (70-c, 70+c),...

Rockwell hardness of pins of a certain type is known to have a
mean value of 50 and a standard deviation of 1.4. (Round your
answers to four decimal places.)
(a) If the distribution is normal, what is the probability that
the sample mean hardness for a random sample of 18 pins is at least
51?
(b) What is the (approximate) probability that the sample mean
hardness for a random sample of 45 pins is at least 51?

A geologist has collected 13 specimens of basaltic rock and 13
specimens of granite. The geologist instructs a laboratory
assistant to randomly select 21 of the specimens for analysis.
(a)
What is the pmf of the number of granite specimens selected for
analysis? (Round your probabilities to four decimal places.)
x
p(x)
(b)
What is the probability that all specimens of one of the two
types of rock...

Suppose the sediment density (g/cm) of a randomly selected
specimen from a certain region is normally distributed with mean
2.69 and standard deviation 0.84.
(a) If a random sample of 25 specimens is selected, what is the
probability that the sample average sediment density is at most
3.00? Between 2.69 and 3.00? (Round your answers to four decimal
places.)
at most 3.00
between 2.69 and 3.00
(b) How large a sample size would be required to ensure that the
probability...

To obtain information on the corrosion-resistance properties of
a certain type of steel conduit, 45 specimens are buried in soil
for a 2-year period. The maximum penetration (in mils) for each
specimen is then measured, yielding a sample average penetration of
x = 53.3 and a sample standard deviation of s =
4.6. The conduits were manufactured with the specification that
true average penetration be at most 50 mils. They will be used
unless it can be demonstrated conclusively that...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 9 minutes ago

asked 20 minutes ago

asked 23 minutes ago

asked 41 minutes ago

asked 46 minutes ago

asked 52 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago