Respuesta :
Answer:
5.71% probability that less than 60% of the sample would report that they had visited woodland in the previous year
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
For a sampling propotion p in a sample of size n, we have that [tex]\mu = p, \sigma = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this problem, we have that:
[tex]\mu = 0.63, \sigma = \sqrt{\frac{0.63*0.37}{650}} = 0.0189[/tex]
What is the approximate probability that less than 60% of the sample would report that they had visited woodland in the previous year?
This is the pvalue of Z when X = 0.6. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.6 - 0.63}{0.0189}[/tex]
[tex]Z = -1.58[/tex]
[tex]Z = -1.58[/tex] has a pvalue of 0.0571
5.71% probability that less than 60% of the sample would report that they had visited woodland in the previous year
