Question

6.78

eaklast on a weekday 2 and σ 12. According to Chebyshev's UAbility can we assert that between 94 and 190 customers Ill Have breakfast there A student answers the 144 questions coin (a) Use the special formu on a weekday morning? 6.78 on a true-f alse test by flipping a balanced las for the mean and the standard deviation of the binomial distribution to find the values of land ơ for the distribution of the number of correct answers that he or she will get. (b) According to Chebyshev's theorem, what can we assert with a probability of at least 0.96 about the number of correct answers that he or she will get? 6.79 Use Chebyshev's theorem to determine the prohabhiliu

Answer 1

Solution:

Given: A student answers the 144 questions on a true false test by flipping a balanced coin.

A balanced coin means fair coin, that is Probability of head = probability of tail = 0.5

thus p = 0.5 and q = 0.5

Part a) Find mean $\mu$ and standard deviation $\sigma$ by using formulas of Binomial distribution.

$\mu = n \times p$

μ = 144 × 0.5

$\mu = 72$

and

$\sigma = \sqrt{n \times p \times q}$

σ = V144 × 0.5 × 0.5

$\sigma = \sqrt{36}$

$\sigma = 6$

Part b) We have to find values of number of correct answers that student will get using Chebeshev's theorem with probability of at least 0.96

According to Chebeshev's theorem, at least of the data lie within k standard deviations from the mean of the distribution.

172 162

that is:

k:2 1.2

So we have

|-읊) = 0.96 12

(1-0.96) = 1.2

0.04 =

0.04

k- 25

5

Thus we get:

μ-k σ 72-5 × 6-72-30-42

and

μ + k σ = 72 5 × 6 = 72 + 30 = 102

Thus there is at least 0.96 probability that student can answer correct answers between 42 and 102 out of 144.