Question

Part A.

Anystate Auto Insurance Company took a random sample of 356 insurance claims paid out during a 1-year period. The average claim paid was $1560. Assume σ = $232.

Find a 0.90 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

lower limit	$
upper limit	$

Find a 0.99 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

lower limit	$
upper limit	$

Part B.

The method of tree ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population of x values has an approximately normal distribution.

1243

1250

1292

1243

1268

1316

1275

1317

1275

Use a calculator with mean and standard deviation keys to find the sample mean year x and sample standard deviation s. (Round your answers to the nearest whole number.)

x =

s =

Find a 90% confidence interval for the mean of all tree ring dates from this archaeological site. (Round your answers to the nearest whole number.)

lower limit	A.D.
upper limit	A.D.

Answer 1

Part A. Let "X" be the insurance claims paid out during a 1-year period.

Given: n=356

, σ = $232

a) The 90% confidence interval for the mean claim payment is given by:

### By using z table z_0.05=1.64

Therefore,

Lower limit=$1539.84

Upper limit=$1580.17

b)

The 99% confidence interval for the mean claim payment is given by:

### By using z table z_0.005=2.58

Therefore,

Lower limit=$1528.276

Upper limit=$1591.724

Part B) Let "X" be the tree ring dates from this archaeological site.

### By using excel function:

=AVERAGE(A1:A9)

s=28.40

s=28

### By using function: =STDEV(A1:A9)

A 90% confidence interval for the mean of all tree ring dates from this archaeological site is given by:

### By using t table: t_0.05,8=1.86

Therefore,

Lower limit=1258 A.D.

Upper limit=1992 A.D.