We are given that a recent survey found that 30% of telephone users have switched completely to cell phone use (i.e. they do not have landlines in their homes).

A random sample of 10 of these customers is selected.

The above situation can be represented through binomial distribution;

$P(X = r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r}; x = 0,1,2,3,......$

where, n = number of trials (samples) taken = 10 customers

r = number of success = 30% of 10 = 3

p = probability of success which in our question is the probability

that telephone users do not have landlines in their homes,

i.e. p = 30%

Let X = Number of telephone users who do not have landlines in their homes

So, X ~ Binom(n = 10, p = 0.30)

Now, the probability that exactly 30% of these 10 telephone users do not have landlines in their homes is given by = P(X = 3)

P(X = 3) = $\binom{10}{3}\times 0.30^{3} \times (1-0.30)^{10-3}$

= $120 \times 0.30^{3} \times 0.70^{7}$

= 0.2668

4 0

3 years ago

What is least perimeter of a rectangle with an area 32 square feet

Aleks04 [339]

If you have a rectangle with an area of 32 square feet, it means that the sides are
A=L x W, 32= 8*4, where
L=8, W=4
other options are
L=16, W=2 and the last one is
L=32, W=1
You need to find the least perimeter , and you know that the perimeter is P= 2(L+W)
Perimeter (1)= 2(8+4)=2*12=24
Perimeter(2)= 2(16+2)=2*18=36
Perimeter (3)=2(32+1)=2*33=66

The least perimeter is 24, with the sides L=8 and W=4

5 0

4 years ago