A simple experiment with a random sample of 10 mathematics students were found to have the following heights (in cm). 155, 185, 175, 175, 173, 170, 169, 164, 161, 185 Assume the heights of mathematics...

Extracted text: A simple experiment with a random sample of 10 mathematics students were found to have the following heights (in cm). 155, 185, 175, 175, 173, 170, 169, 164, 161, 185 Assume the heights of mathematics students are independently and normally distributed X ~ N(0,0²) with a known variance of o² =99.12 cm². (a) Calculate a point estimate of the mean height 0 and a probability that this estimate is exactly equals to the true value of 0. (b) Compute the standard error, ơ/\n of the sample mean by using given variance. Estimate an equal-tailed 90% confidence interval for 0 by using the sample mean and its standard error. (c) (d) Calculate an equal-tailed 50% confidence interval for 0.