Question

Pet Owners: As of May 2018, dogs accounted for 68% of all pets owned (between dogs and cats). For a random sample of 750 pet owners

1) Find the probability that in a random sample of 750 pet owners more than 154 own dogs

2) Find the probability that in a random sample of 750 pet owners exactly 278 own dogs

3) Find the probability that in a random sample of 750 pet owners that at the most 354 own dogs

4) Find the mean of the number out of 750 pet owners have dogs as their pet

Answer 1

X ~ Bin ( n , p)

Where n = 750 , p 0.68

Mean = n * p = 750 * 0.68 = 510

Standard deviation = sqrt [ n p ( 1 - p) ]

= sqrt [ 750 * 0.68 ( 1 - 0.68) ]

= 12.7750

a)

Using normal approximation,

P(X < x) = P(Z < ( x - Mean) / SD)

With continuity correction,

P(X > 154) = P(Z > (154.5 - 510) / 12.7750)

= P(Z > -27.83)

= P(Z < 27.83)

= 1 (From Z table)

b)

P(X = 278) = P(277.5 < X < 278.5) (With continuity correction)

= P(X < 278.5) - P(X < 277.5)

= P(Z < ( 278.5 - 510) / 12.7750) - P(Z < ( 277.5 - 510) / 12.7750)

= P(Z < -18.12) - P(Z < -18.20)

= 0 - 0 (From Z table)

= 0

c)

P(X <= 354) = P(Z < 354.5 - 510) / 12.7750)

= P(Z < -12.17)

= 0 (From Z table)

d)

Mean = n * p = 750 * 0.68 = 510