Answer :
The probability that the sample proportion will be greater than 0.34 is P(Z≤1.8).
The chance of the pattern share below the regular chance is calculated via way of means of the z-check statistic of 1 pattern share. An excel feature of the same old regular distribution, NORMDIST() is used to get the desired probabilities.
Given that, Population share, p=zero.25
Sample size, n=seventy five
- The required chance is P(^p>zero.34).
- Now,
- P(^p>zero.34)=1−P(^p−p√p(1−p)n≤zero.34−p√p(1−p)n)P(^p>zero.34)=1−P(Z≤zero.34−zero.25√zero.25(1−zero.25)seventy five)P(^p>zero.34)=1−P(Z≤1.8)
- Excel feature for the above chance:
- =NORMDIST(1.8,zero,1,1)
- P(^p>zero.34)=1−zero.964P(^p>zero.34)=zero.036
- The required chance is P(zero.196<^p<zero>
- Now,
- P(zero.196<^p<zero n)P(zero.196<^p<zero.354)=P(zero.196−zero.25√zero.25(1−zero.25)/seventy five P(zero.196<^p<zero.354)=P(−1.08 Z<2.08)P(zero.196<^p<zero.354)=P(Z>Excel feature for the above chance:
- =NORMDIST(2.08,zero,1,1)
- =NORMDIST(-1.08,zero,1,1)
- P(zero.196<^p<zero P(zero.196<^p<zero.354)=zero.841>
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