A level Math Qn

Pinkbow6826 SG

Need Help!!!

In a certain college, a proportion p of its students own an iphone. A sample of 10 students is taken at random. The random variable X denotes the number of students who own an iPhone.

(i) Comment on the stability of using the binomial probability distribution to model this situation and state an assumption used.

(ii) Write down an expression for P(X=4) in terms of p.

(iii) It is given that the valur of P(X=4) is 0.2 and p<0.5. Show that the value of p is 0.3 (correct to 1 decimal place).

(iv) Another sample of 60 students is taken. Using a suitable approximation, estimate the probability that the sample contains less than 20 students who own an iPhone.

Thanks!!

wee_ws SG

Hi,

What specific difficulty are you facing? Thanks.

Cheers,
Wen Shih

frekiwang SG

(ii)

P(X=4)=10C4 x p^4 x (1-p)^6

(iii)

LHS=P(X=4)=0.2

RHS=10C4 x 0.3^4 x 0.7^6 = 0.200120949 = 0.2 approximately

Shown

(iv) Let Y denote the number of students who own Iphones.

np=60x0.3=18, npq=60x0.3x0.7=12.6

Y~B(60,0.3)~N(18,12.6) approximately

P(Y<20) = P(Y<19.5) = .... use GC or Normal Table to compute the value please.

Pinkbow6826 SG

I have difficulty showing that p is 0.3. can this be done using the GC?

wee_ws SG

Hi,

The approach by frekiwang is not correct, as 0.3 is being verified via substitution. To show means to find it by algebra or by graphical means.

Given: P(X = 4) = 0.2

1. Use GC to find the intersection between two graphs y = 0.2 and y = expression obtained in (ii). For window settings, use 0 <= X <= 1 and 0 <= Y <= 1.

2. Accept one of the solutions, since p < 0.5.

Thanks.

Cheers,
Wen Shih