Question

A study conducted by the Pew Research Center reported that 58% of cell phone owners used their phones inside a store for guidance on purchasing decisions. A sample of 15 cell phone owners is studied. What is the probability that 10 or more of them used their phones for guidance on purchasing decisions? Round your answer to 2 decimal places

Answer 1

Answer:

The probability that 10 or more of them used their phones for guidance on purchasing decisions = $P(X\geq10 )$   = .278

Step-by-step explanation:

Given -

A study conducted by the Pew Research Center reported that 58% of cell phone owners used their phones inside a store for guidance on purchasing decisions .

Then the probability of success is (p) = 58$\%$ = .58

the probability of failure is (q) = 1 - p = .42

sample size n = 15

Let X be the no of owners used their phones for guidance on purchasing decisions

Using the formula

$P(X = r )= \binom{n}{r}(p)^{r}(q)^{n - r}$

The probability that 10 or more of them used their phones for guidance on purchasing decisions = $P(X\geq10 )$  

= P(X = 10) +  P(X = 11) +  P(X = 12) +  P(X = 13) +  P(X = 14) +  P(X = 15)

= $\binom{15}{10}(.58)^{10}(.42)^{15 - 10} + \binom{15}{11}(.58)^{11}(.42)^{15 - 11} + \binom{15}{12}(.58)^{12}(.42)^{15 - 12} + \binom{15}{13}(.58)^{13}(.42)^{15 - 13} + \binom{15}{14}(.58)^{14}(.42)^{15 - 14} + \binom{15}{15}(.58)^{15}(.42)^{15 - 15}$= $\binom{15}{10}(.58)^{10}(.42)^{5} + \binom{15}{11}(.58)^{11}(.42)^{4} + \binom{15}{12}(.58)^{12}(.42)^{3} + \binom{15}{13}(.58)^{13}(.42)^{2} + \binom{15}{14}(.58)^{14}(.42)^{1} + \binom{15}{15}(.58)^{15}(.42)^{0}$

= $\frac{15!}{(10!)(5!)}(.58)^{10}(.42)^{5} + \frac{15!}{(10!)(5!)}(.58)^{11}(.42)^{4} + \frac{15!}{(10!)(5!)}(.58)^{12}(.42)^{3} + \frac{15!}{(10!)(5!)}(.58)^{13}(.42)^{2} + \frac{15!}{(10!)(5!)}.58)^{14}(.42)^{1} + \frac{15!}{(10!)(5!)}(.58)^{15}(.42)^{0}$=

$2002\times.0043\times.013 + 1365\times.0024\times.031 + 455\times.00144\times.074 + 105\times.00084\times.17 + 15\times.00048\times.42 + 1\times.00028\times1$

= .1119 + .1015 + .048 + .014 + .0030 + .00028

= .278

Answer 2

Answer: A study conducted by the Pew Research Center reported that 58% of cell phone owners used their phones inside a store for guidance on purchasing decisions. A sample of 15 cell phone owners is studied. What is the probability that 10 or more of them used their phones for guidance on purchasing decisions? Round your answer to 2 decimal places

Step-by-step explanation: