Question

A recent study estimates that 45% of iPhone still have their phone their phone within 2 years of purchasing it. Suppose you randomly select 30 iPhone users. Let random variable X denote the number of iPhone users who still have their original phone after 2 years.

Describe the probability distribution of X (Hint: Give the name of the distribution and identify n and p).

Find the expected value of X. Round to 1 decimal place.

Find the standard deviation of X. Round to 3 decimal places.

Determine the probability that X equals 13. Round to 3 decimal places.

Determine the probability that EXACTLY 11 iPhone users still have their original phone after 2 years. Round to 3 decimal places.

Determine the probability that at most 5 iPhone users still have their original phone after 2 years. Round to 3 decimal places.

Determine the probability that at least 8 iPhone users still have their original phone after 2 years. Round to 3 decimal places.

Determine the probability that between 6 and 9 iPhone users still have their original phone after 2 years. Round to 3 decimal places.

Answer 1

Solution:

a) Mean = Expected Value = μ_x̅ = n•p = (30)(0.45) = 13.5

n•p•(1 - p) = (30)(0.45)(1 - 0.45) = 7.425

b) Standard Deviation = σ_x̅ = √ n•p•(1 - p) = √7.425 = 2.7248

c)

the probability that X equals 13

d)  the probability that EXACTLY 11 iPhone users P(11) =0.098

*** Dear student we answer four sub parts once post remaining separately****