contestada

In order to gain additional information about respondents, some marketing researchers have used ultraviolet ink to precode questionnaires that promise confidentiality to respondents. of 205 randomly selected marketing researchers who participated in an actual survey, 117 said that they disapprove of this practice. suppose that, before the survey was taken, a marketing manager claimed that at least 65 percent of all marketing researchers would disapprove of the practice. (a) assuming that the manager's claim is correct, calculate the probability that 117 or fewer of 205 randomly selected marketing researchers would disapprove of the practice. use the normal approximation to the binomial. (round your z answers to 2 decimal places. round your answer to 4 decimal places. round the mean and standard deviation to 4 decimal places.)

Respuesta :

The probability that 117 or fewer of 205 randomly selected marketing researchers would disapprove of the practice = 0.0104.

What is Normal Approximation?

When the sample size is large, the binomial distribution is employed instead of the normal approximation since the calculation becomes more complicated when the sample size is large.

Now,

  • The majority of marketing researchers—at least 65 percent—are against the practice.
  • The percentage of marketing researchers overall who would be against the approach is around 65%.

Let the sample size be n and the number of people who disapprove of the practice be x.

Then, n = 205, x = 117

Then, by normal approximation, the value of mean (μ) will be given by:

μ = np = 205(0.65) = 133.25

Standard deviation (σ) = [tex]\sqrt{np(1-p)}[/tex]

σ = 205(0.65)(1 - 0.65) = 133.25(0.35) = 6.83

The probability that 117 or fewer of 205 randomly selected marketing researchers would disapprove of the practice:

P(x ≤ 117) = P (x < 117 + 0.5) (By Continuity correction Factor)

=> P(x ≤ 117) = P ( x < 117.5)

=> P(x ≤ 117) = P ( z < [tex]\frac{117.5 - 133.25}{6.83}[/tex])

=> P(x ≤ 117) = P ( z < -2.31)

=> P(x ≤ 117) = 0.0104

Hence, the probability that 117 or fewer of 205 randomly selected marketing researchers would disapprove of the practice = 0.0104.

To learn more about normal approximation, refer to the link: https://brainly.com/question/2193433

#SPJ4