Question

Of all vehicles sold by a certain car dealership, 35% are sports cars. From 50 randomly selected vehicle purchases, use the normal distribution to approximate the probability that less than 14 are sports cars.

a) 0.1178
b) 0.1497
c) 0.0911
d) 0.1869

Answer 1

a) 0.1178

Step-by-step explanation:

The calculation is shown below:-

Mean = np

= 50 × 0.35

= 17.5

Standard deviation is

=
`√(n* p* q)`

=
`√(50* 0.35 * 0.65)`

= 3.373

Therefore, as we know that

P which is Less than 14

So,

= P(X < 13.5)

= P(z < (13.5 - 17.5) ÷ 3.373

= P(z < -1.186)

= 0.1178

Hence, the correct option is a. 0.1178

basically we used the above formulas i.e mean and standard deviation