Fundamentals of Probability and Statistics for Engineers

Example 9.19.Problem: let us assume that the annual snowfall in the Buffalo
area is normally distributed. Using the snowfall record from1970–79 as given
in Problem 8.2(g) (Table 8.6, page 257), determine a 95% confidence interval
for mean m.
Answer: for this example, the observed sample mean is

and the observed sample variance is

Using Table A.4, we find that Substituting all the values given
above into Equation (9.141) gives

It is clear that this interval would be different if we had incorporated more
observations into our calculations or if we had chosen a different set of yearly
snowfall data.

1–

2 2

fT(t)

t

–tn, / 2 tn, / 2

Figure 9. 8 [100(1 )]% confidence limits for T with n degrees of freedom

Parameter Estimation 301

α

α α

α α



/ /

ˆ 0 :05,nˆ10,

xˆ

1

10

… 120 : 5 ‡ 97 : 0 ‡‡ 97 : 3 †ˆ 112 : 4 ;

s^2 ˆ

1

9

‰… 120 : 5  112 : 4 †^2 ‡… 97 : 0  112 : 4 †^2 ‡‡… 97 : 3  112 : 4 †^2 Š

ˆ 1414 : 3 :

t9, 0: 025 ˆ 2 :262.

P… 85 : 5 <m< 139 : 3 †ˆ 0 : 95 :