Question

Due Mon 0vn MA 120 Basic Statistics Homework Assignment 2 PLEASE SHOW ALL WORK ON SEPARATE PAPER. Do your own work. Pollow instructions. Point values are in parentheses 1, suppo sex is binomial with n 25, p - 0.38. (5) (a) Calculate P(x12) (10) (b) Calculate P (9 x 11) c) For this binomial distribution, calculate the mean , variance and standard deviation (5) 2. On the SAT test, clyde klutz achieved a score of 387. The national mean for the SAT test was 554; the standard deviation was 82. Calculate Clyde's z-score (standard units). 3. Assume z is standard normal. Calculate the following probabilities. (7) (a) P (-0.37 z 1.47) Include a labeled, shaded diagram (7) (b) P(z <-0.08) Include a labeled, shaded diagram (7) (c) P(z > 1.73) Include a labeled shaded diagram. (10) 4. Assume x is normal with ?- 89.5 and ?= 4.6. Calculate P(87 94). Include a labeled, shaded diagram 5. Let x be binomial with n = 15, p : 0.60 (5) (a) calculate Pix 9) s (5) (b) calculate P(9 sx 12) (5) (c) Calculate P(x 8) (15) 6. P(x) 20 0.34 25 0.27 30 0. 21 35 0.18 For this probability distribution, calculate (a) mean (b) variance (c) standard deviation (15) 7. Suppose that x is normal with mean 45.2 and standard deviation d 6.8. A sample of size n 20 is taken. What is the probability that the mean of the sample is between 45 and 50? USE THE CENTRAL LIMIT THEOREM. (20) 8. According to recent surveys, 658 of households have personal computers. If a random sample of 200 households is selected, what is the probability that more than 140 have a personal computer? USE THE NORMAL APPROXIMATION TO THE BINOMIAL.

Answer 1

a)

$P(X=x) = \binom{n}{x}p^x(1-p)^{n-x}$

$P(X=12) = \binom{25}{12}0.38^{12}(1-0.38)^{25-12} = 0.0943$

b)

$P(9\leq X\leq 11) = P(X=9)+P(X=10)+P(X=11) = 0.1609+0.1578+0.1319 = 0.4506$

c)

$\mu = np =25*0.38 = 9.5$

$\sigma^2 = np (1-p) = 25*0.38*(1-0.38) = 5.89$

$\sigma= \sqrt{np (1-p)} = 2.427$

2)

$z = \frac{x-\mu}{\sigma} = \frac{387-554}{82} = -2.036$