Question

Please show all work and explain your work!

1.) Consider the following sample of observations on coating thickness for low-viscosity paint.

Assume that the distribution of coating thickness is normal (a normal probability plot strongly supports this assumption).

0.82 | 0.88 | 0.88 | 1.05 | 1.09 | 1.22 | 1.29 | 1.31 | |||||||

1.45 | 1.49 | 1.59 | 1.62 | 1.65 | 1.71 | 1.76 | 1.83 |

(a) Calculate a point estimate of the value that separates the
largest 10% of all values in the thickness distribution from the
remaining 90%. [*Hint*: Express what you are trying to
estimate in terms of μ and σ.] (Round your answer to four decimal
places.)

(b) Estimate *P*(*X* < 1.4), i.e., the
proportion of all thickness values less than 1.4. [*Hint*:
If you knew the values of *μ* and *σ*, you could
calculate this probability. These values are not available, but
they can be estimated.] (Round your answer to four decimal
places.)

(c) What is the estimated standard error of the estimator that
you used in part (b)? (Round your answer to four decimal
places.)

Answer #1

from the given data,

mean = 1.3525

s = 0.3347

a)

t-value = 1.3406

x = 1.3525 + 1.3406*0.3347/sqrt(16)

x = 1.4647

b)

P(X < 1.4)

P(t < (1.4 - 1.3525)/(0.3347/sqrt(16)))

= P(t < 0.5677)

= 0.7107

c)

std.error = (0.3347/sqrt(16))

= 0.0837

The above solutions were done using t-values because population std. dev. was unknown and sample size is less than 30.

Solving below using z-values

from the given data,

mean = 1.3525

s = 0.3347

a)

z-value = 1.28

x = 1.3525 + 1.28*0.3347/sqrt(16)

x = 1.4596

b)

P(X < 1.4)

P(z < (1.4 - 1.3525)/(0.3347/sqrt(16)))

= P(z < 0.5677)

= 0.7149

c)

std.error = (0.3347/sqrt(16))

= 0.0837

Consider the following sample of observations on coating
thickness for low-viscosity paint.
0.83
0.88
0.88
1.07
1.09
1.15
1.29
1.31
1.34
1.49
1.59
1.62
1.65
1.71
1.76
1.83
Assume that the distribution of coating thickness is normal
(a) Calculate a point estimate of the mean value of coating
thickness.
1.343125
(b) Calculate a point estimate of the median of the coating
thickness distribution.
1.325
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