Let X be normally distributed with mean 120 and standard deviation 10. What is the probability P(X < 125|X < 130)? 12 B) 0.42 C) 0.43 D) 0.04 E) 0.82 Ten students are taking a course at NTNU. Each student has a probability of 0.5 of showing up at any given lecture and they act independently. What is the probability that exactly four students attend a given lecture? 246 B) 0.623 C) 0.011 D) 0.377 E) 0.205 Let X be a discrete random variable with distribution x 0 1 2 3 P(X = x) 0.1 0.5 0.3 0.1 What is the expected value of X? 5 B) 1.4 C) 2.6 D) 0.8 E) 1.0 Let X be a discrete random variable with distribution x 0 1 2 3 P(X = x) 0.1 0.5 0.3 0.1 What is the standard deviation of X? 5 B) 1.4 C) 2.6 D) 0.8 E) 1.0

 

Find the correct answer to each question. The calculation need not be included.

  1. Let X be normally distributed with mean 120 and standard deviation 10. What is the probability P(X < 125|X < 130)?
    1. 12 B) 0.42 C) 0.43 D) 0.04 E) 0.82
  2. Ten students are taking a course at NTNU. Each student has a probability of 0.5 of showing up at any given lecture and they act independently. What is the probability that exactly four students attend a given lecture?
    1. 246 B) 0.623           C) 0.011           D) 0.377          E) 0.205
  3. Let X be a discrete random variable with distribution

x   0          1          2          3

P(X = x) 0.1     0.5       0.3       0.1

What is the expected value of X?

  1. 5 B) 1.4   C) 2.6   D) 0.8  E) 1.0
  1. Let X be a discrete random variable with distribution

x   0          1          2          3

P(X = x) 0.1     0.5       0.3       0.1

What is the standard deviation of X?

  1. 5 B) 1.4   C) 2.6   D) 0.8  E) 1.0

Problem 2

A randomized clinical trial was performed to compare two dierent treatments for tennis elbow: steroid injection and physiotherapy. Six weeks after treatment the pain-free grip force x was measured. Assume that x is normally distributed, with mean µ1 and standard deviation σ1 for pasients given steroid injection, and with mean µ2 and standard deviation σ2 for patients given physiotherapy.

  1. a) Propose a test of whether mean pain-free grip force for patients given steriods is equal to that of patients given physiotherapy. State the null hypothesis and the alternative hypothesis.

A number n1 = 62 patients were given steroid injections. The sample average for pain-free grip force was x¯1 = 83.6 and the sample standard deviation was s1 = 22.9. A number n2 = 65 patients were given physiotherapy. The sample average for pain-free grip force was x¯2 = 70.2 and the sample standard deviation was s2 = 25.4.

  1. Test whether mean pain-free grip force for patients given steriods and mean pain-free grip force for patients given physiotherapy are equal. Use signicance level 5 %.
  2. Find a 95% condence interval for µ1 µ2. How do you interpret this interval?

Problem 3

Children in the fourth, fth and sixth grade were asked what they considered important at school. The possible answers were ’good marks’, ’success in sports’ and ’popularity’.

The answers distributed as below:

4th grade      5th grade        6th grade        total good marks        49       50        69        168 success in sports 19       22        28      69 popularity   24       36        38        98 totalt          92       108      135      335

  1. Propose a test of whether answer and grade are associated, stating the null hypothesis and the alternative hypothesis.
  2. Perform the proposed test at the 5% signicance level.
  3. Find a 95% condence interval for the proportion that answers ’good marks’ among 6 th graders.
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