Question

Suppose the number of radios in a household has a binomial distribution with parameters ?=21 and ?=35%.

Find the probability of a household having:

(a) 7 or 17 radios
(b) 15 or fewer radios
(c) 13 or more radios
(d) fewer than 17 radios
(e) more than 15 radios

Answer 1

This is a binomial distribution question with
n = 21
p = 0.35
q = 1 - p = 0.65
This binomial distribution can be approximated as Normal distribution since
np > 5 and nq > 5

Since we know that


a)


b)
The z-score at x = 15.5 is,

This implies that

c)

The z-score at x = 12.5 is,

This implies that



d)
P(x < 17.0)=?
The z-score at x = 17.0 is,

This implies that


e)
P(x > 15.0)=?
The z-score at x = 15.0 is,

This implies that

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