Question

A study conducted by the PEW Research Center reported that 62% of cell phone owners used their phones inside a store for guidance on purchasing decisions. A random sample of 13 cell phone owners is studied to understand how cell phones are used to make purchasing decisions. Write all answers as a decimal rounded to the fourth. a) Interpret the mean using the word expect. b) Find the standard deviation c) Find the probability of exactly 7 using their phones to make purchase decisions. Do this by hand and show your work. Please reference lecture examples for the amount of work to show. d) Find the probability less than 4 use their phones to make purchasing decisions. e) Find the probability at least 8 use their phones to make purchasing decisions.

Answer 1

a)

Here, μ = n*p = 8.06,

cell phone owners is studied to understand how cell phones are used to make purchasing decision is 8.06

b)
σ = sqrt(np(1-p)) = 1.7501

c)

Here, n = 13, p = 0.62, (1 - p) = 0.38 and x = 7
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 7)
P(X = 7) = 13C7 * 0.62^7 * 0.38^6
P(X = 7) = 0.1820

d)

Here, n = 13, p = 0.62, (1 - p) = 0.38 and x = 4
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X <4).
P(X <4) = (13C0 * 0.62^0 * 0.38^13) + (13C1 * 0.62^1 * 0.38^12) + (13C2 * 0.62^2 * 0.38^11) + (13C3 * 0.62^3 * 0.38^10)
P(X <4) = 0 + 0.0001 + 0.0007 + 0.0043
P(X < 4) = 0.0051

e)

Here, n = 13, p = 0.62, (1 - p) = 0.38 and x = 8
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X >= 8).
P(X <= 7) = (13C0 * 0.62^0 * 0.38^13) + (13C1 * 0.62^1 * 0.38^12) + (13C2 * 0.62^2 * 0.38^11) + (13C3 * 0.62^3 * 0.38^10) + (13C4 * 0.62^4 * 0.38^9) + (13C5 * 0.62^5 * 0.38^8) + (13C6 * 0.62^6 * 0.38^7) + (13C7 * 0.62^7 * 0.38^6)
P(X <= 7) = 0 + 0.0001 + 0.0007 + 0.0043 + 0.0175 + 0.0513 + 0.1115 + 0.182
P(X <= 7) = 0.3674

P(x >=8)= 1 - P(x < =7)
= 1 - 0.3674
= 0.6326