A construction crew is lengthening a road that originally measured 45 miles. The crew is adding one mile to the road each day.
1 answer:
You might be interested in
Answer:
0.88% probability that the sample proportion will differ from the population proportion by more than 5%
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
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 proportions p in a sample of size n, we have that
In this problem:
What is the probability that the sample proportion will differ from the population proportion by more than 5%?
Less than 0.19 - 0.05 = 0.14 or greater than 0.19 + 0.04 = 0.24. Since the normal distribution is symmetric these probabilities are equal, which means that we can find one of them and multiply by 2. So
Probability of being less than 0.14.
pvalue of Z when X = 0.14. So
has a pvalue of 0.0044
2*0.0044 = 0.0088
0.88% probability that the sample proportion will differ from the population proportion by more than 5%