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← 6 ANN X o 1 19°C Sunny of 1 Q rese: X R (PDF X D Clim x a Hom X Assic X Qcher X C Cher X assic X ident X File | C:/Users/thabo/OneDrive/Desktop/Homework8.pdf 2) Page view A Read aloud | Add text V Draw Statistical Foundations of Data Science Homework 8 Due Friday May 6 The content of this assignment is based on the eighth lecture in the course titled "The Normal distribution". 1. Various students take different IQ tests. These tests may be on different scales, that is may have different means and variances. However in all cases the distributions will be normal a Albus gets a Z-score of 3.5. The mean on his test was 110 and the variance 144. Find Albus's score [4] b Voldemort scores 2 standard deviations below normal with a score of 70 on a test with mean 100. Find the standard deviation of scores on the test [4] e Hagrid scores 0.5 standard deviations below the mean. If the tests variance is 100 and Hagrid scored 105 find the tests' mean [4] d Harry scores right on the mean with a of 90. Find his Z-score [4] 2. The binomial distribution is a sum of IID random variables and is therefore approximately normal large n and fixed p. In our question a fair coln (p=0.5) is flipped one million times. The random variable counting the number of heads is called X. a Compute E[X] [3] b Compute V(X) [3] e Compute the standard deviation of X (3) d Use the CLT to estimate P(499500 < X < 501000) [5] 1 Da X C Dash X Highlight Get X to Hom X Erase 33 ENG US + 8 ☎ dù € A ✓ 203 14:24 2022/05/02 ¹2