7 The heights, in centimetres, of adult females in Litania have mean \(\mu\) and standard deviation \(\sigma\). It is known that in 2004 the values of \(\mu\) and \(\sigma\) were 163.21 and 6.95 respectively. The government claims that the value of \(\mu\) this year is greater than it was in 2004. In order to test this claim a researcher plans to carry out a hypothesis test at the \(1 \%\) significance level. He records the heights of a random sample of 300 adult females in Litania this year and finds the value of the sample mean.

1. State the probability of a Type I error.
   \includegraphics[max width=\textwidth, alt={}]{ff3433b0-baab-45e3-845e-56a794739bba-12_74_1577_557_322} ........................................................................................................................................ You should assume that the value of \(\sigma\) after 2004 remains at 6.95 .
2. Given that the value of \(\mu\) this year is actually 164.91 , find the probability of a Type II error.
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