A pharmaceutical company produces tablets. The mass, X X\,X mg, of the tablets follows a normal distribution N(μ,32)N(\mu, 3^2)N(μ,32). To monitor the production process, a random sample of n n\,n tablets is selected and tested at the 5% level of significance using the following hypotheses:
H0:μ=250andH1:μ>250 H_0 : \mu = 250 \quad \text{and} \quad H_1 : \mu > 250 H0:μ=250andH1:μ>250Find, in terms of nnn, the critical region of the test.
The probability of a Type II error, when the true mean is μ=252\mu = 252μ=252, is less than 0.10.
Find the minimum value of nnn.
