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roseemariehunter12
27.03.2020 •
Mathematics
Based on historical data, your manager believes that 29% of the company's orders come from first-time customers. A random sample of 169 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.24 and 0.46
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Ответ:
Probability that the sample proportion is between 0.24 and 0.46 is 0.936.
Step-by-step explanation:
We are given that based on historical data, your manager believes that 29% of the company's orders come from first-time customers.
A random sample of 169 orders will be used to estimate the proportion of first-time-customers.
Let
= sample proportion
Now, the z score probability distribution for sample proportion is given by;
Z =
~ N(0,1)
where, p = % of the company's orders that come from first-time customers = 29%
n = sample of orders = 169
So, probability that the sample proportion is between 0.24 and 0.46 is given by = P(0.24 <
< 0.46) = P(
< 0.46) - P(
0.24)
P(
< 0.46) = P(
<
) = P(Z < 4.4) = 0.99999
P(![\hat p](/tpl/images/0566/9646/7e39a.png)
0.24) = P( ![\frac{\hat p -p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }](/tpl/images/0566/9646/2c82f.png)
![\leq](/tpl/images/0566/9646/46cd6.png)
) = P(Z
-1.52) = 1 - P(Z < 1.52)
= 1 - 0.93574 = 0.06426
Therefore, P(0.24 <
< 0.46) = 0.99999 - 0.06426 = 0.936
Hence, probability that the sample proportion is between 0.24 and 0.46 is 0.936.
Ответ: