Question

The concerns about the impact of technology on our lives are growing. There have been recent research reports about the negative impact of digital technology usage on​ stress, work​ productivity, happiness, and overall​ well-being. In light of these​ concerns, a polling organization asked technology experts about their opinion on our digital life and found that 29% of the experts believe that in the future our lives will be more harmed than helped by their digital environment. In an effort to confirm these​ results, a local tech company decides to ask 190 randomly selected customers their opinions about their digital life. Answer parts a through c below.

A. What is the probability that 35 or more people from this sample are concerned about the digital​ environment?

The probability is =

​(Round to four decimal places)

B. What is the probability that 45 or more people from this sample are concerned about the digital​ environment?

The probability is =

​(Round to four decimal places)

(please round to the correct decimal places)

Answer 1

(A)

(B)

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We use the binomial to normal approximation to calculate the probabilities.

The result says If X is binomial with parameters n and p, then for large n, .

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Let X be the number of people concerned about the digital​ environment in 190 randomly selected customers . So we take n=190.

Since 29% of the experts believe that in the future our lives will be more harmed than helped by their digital environment, we can take probability that an individual is concerned about the digital​ environment, p=29%=0.29.

Then X has binomial distribution with n=190 and p=0.29.

__________________________

(A)

We want to find the probability that 35 or more people from this sample are concerned about the digital​ environment

________________________

(B)

We want to find the probability that 45 or more people from this sample are concerned about the digital​ environment