QUESTION 1 A politician claims that the mean salary for engineering managers in his state is more than the national mean

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QUESTION 1
A politician claims that the mean salary for engineering
managers in his state is more than the national mean, AU$ 82,000.
Assume that the population of all engineering salaries in the
country is normally distributed, with a standard deviation = AU$
8,400. The salaries for a random sample of 30 engineering managers
in the state of this politician resulted in a mean of AU$ 84,439.
Is there enough evidence to support the claim at the 1%
significance level?
QUESTION 2
The average life of a certain type of motor is 10 years,
with a standard deviation of 2 years. If the manufacturer is
willing to replace only 3% of the motors that fail, how long a
guarantee should he offer? Assume that the lives of the motors
follow a normal distribution.