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I am Lyosha [343]
3 years ago
15

your manager believes that 43% of the company's orders come from first-time customers. A random sample of 98 orders will be used

to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.33 and 0.46?
Mathematics
1 answer:
Tpy6a [65]3 years ago
5 0

Answer: 0.7030

Step-by-step explanation:

Given : The population proportion for company's orders come from first-time customers : p=0.43

Sample size : n= 98

The test statistic for population proportion:-

z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}

For , \hat{p}=0.33

z=\dfrac{0.33-0.43}{\sqrt{\dfrac{0.43(1-0.43)}{98}}}\approx-2.00

For , \hat{p}=0.46

z=\dfrac{0.46-0.43}{\sqrt{\dfrac{0.43(1-0.43)}{98}}}\approx0.60

\text{The p-value =}P(-2.00

Hence, the probability that the sample proportion is between 0.33 and 0.46 is 0.7030.

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