Let X1, X2, X3,..., X, be a random sample from a distribution with known variance Var(X,) = o?, and unknown mean EX, = 0. Find a (1 – a) confidence interval for 0. Assume that n is large. %3D

IQs measured on a certain scale are normally distributed with a mean of 90 and a variance of 400. whats the probability that a random person will have an IQ between 120 and 130.   the IQ of 51 people was taken, a sample mean of 90 and standard deviation of 64 was obtained. does this support that people tend to have IQs<100? use a 5% level of significance.

Suppose a random sample of 25 students is selected from a community college where the scores on the final exam (out of 125 points) are normally distributed having mean equal to 112 and standard deviation equal to 4. Find the probability that the sample mean deviates from the population mean µ = 112 by no more than 3.

Let x be a random variable that represents the pH of arterial plasma (l.e., acidity of the blood). For healthy adults, the mean of the x distribution is = 7.4.t A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 31 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.8 with sample standard deviations = 3.3. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood. A USE SALT (a) What is the level of significance? State the null and alternate hypotheses. O Hg: u + 7.4; H,: = 7.4 O Hg: H = 7.4; H,: H > 7.4 O H,: H = 7.4; H,i 7.4; H,: H = 7.4 O H: = 7.4; H,: H# 7.4 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since the sample size is large a is known. O The standard normal, since the sample size is large and a is known. O The standard normal,…