Sunday

August 30, 2015
Posted by **Nora 512** on Saturday, June 1, 2013 at 6:52pm.

Consider the following binomial random variables.

(a) The number of tails seen in 47 tosses of a quarter.

(i) Find the mean. (Give your answer correct to one decimal place.)

(ii) Find the standard deviation. (Give your answer correct to two decimal places.)

(b) The number of left-handed students in a classroom of 59 students (assume that 17% of the population is left-handed).

(i) Find the mean. (Give your answer correct to one decimal place.)

(ii) Find the standard deviation. (Give your answer correct to two decimal places.)

- Math -
**Nora 512**, Saturday, June 1, 2013 at 11:42pmI have 24 questions like the two above and if anyone can help I will use them as examples and work the other ones. I do so much better with examples. Thank you

- Math -
**MathMate**, Sunday, June 2, 2013 at 9:32amFor a binomial distribution with N bernoulli trials with probability of success p (i.e. failure q = 1-p),

the following properties can be proved:

mean = Np

variance = Npq

Take the square-root of variance to get standard deviation.

In 15 tosses of a fair dime, N=15, p=0.5, q=1-0.5=0.5

so mean = 15*0.5=7.5

standard deviation = sqrt(Npq)=√(15*.5*.5)=1.936

- Math -
**Nora 512**, Sunday, June 2, 2013 at 11:37amThank you, I have worked 3 out like the first one, but how do you do one with % just show me example as the one above, don't have to use those numbers just something I can go by...I did get the other 3 I worked out right..Thanks again

- Math -
**MathMate**, Sunday, June 2, 2013 at 11:52am17% are left-handed means

P(left-handed)=0.17

(remember 17%=17/100=0.17)

so

N=59, p=0.17, q=1-0.17=0.83

you can take it from here!

- Math check -
**Nora 512**, Sunday, June 2, 2013 at 12:21pmOk I have got this far and missed the last two on standard deviation, can you look at these and tell me how I missed them?

(23) The number of cars found to have unsafe tires among the 379 cars stopped at a roadblock for inspection (assume that 15% of all cars have one or more unsafe tires).

(i) Find the mean. (Give your answer correct to one decimal place.)

Correct: Your answer is correct. .

56.9 by 379 x .15 =

(ii) Find the standard deviation. (Give your answer correct to two decimal places.)

Incorrect: Your answer is incorrect. . answer 6.79 by sqrt(379 x .15x.81)

(24) The number of melon seeds that germinate when a package of 60 seeds is planted (the package states that the probability of germination is 0.89.

(i) Find the mean. (Give your answer correct to one decimal place.)

Correct: Your answer is correct. 53.40 by 60 x 0.89 =

(ii) Find the standard deviation. (Give your answer correct to two decimal places.)

Incorrect: Your answer is incorrect. sqrt(60 x .89x.18) = 3.07 and tried again 3.10

- Math -
**MathMate**, Sunday, June 2, 2013 at 12:37pmFor 23)(ii) I have

σ=√(npq)=√(379*0.15*0.85)=6.95

For 24(ii)

p=0.89,

q=1-0.89=0.11

σ=√(npq)

- Math check -
**Nora 512**, Thursday, June 6, 2013 at 5:54pmOk (23) I got the standard deviation as 1.99 and on (24) I got standard deviation as 0.73. I have worked and worked these and I am missing something if this is not right.