4. The following is the distribution of the daily emission of sulfur oxides by an industrial plant. As can easily be verified, the mean of the distribution is 18.85 and its standard deviation is s=5.55. To test the null hypothesis that these data constitute a random sample from a normal population, proceed with the following steps: Tons of Sulfur 5.0-8.99 9.0-12.99 13.0-16.99 17.0-20.99 21.0-24.99 25.0-28.99 29.0-32.99 C. Freq. 3 10 14 25 17 9 2 a. Find the probabilities that a random variable having the normal distribution with u-18.85 and o=5.5 will take on a value less than 8.95, between 8.95 and 12.95, between 12.95 and 16.95, between 16.95 and 20.95, between 20.995 and 24.95, between 24.95 and 28.95, and greater than 28.95. b. Changing the first and last classes of the distribution to "8.95 or less" and "28.95 or more" find the expected normal curve frequencies corresponding to the seven classes of the distribution by multiplying the probabilities obtained in part (a) by the total frequency of 80. Test at the 0.05 level of significance whether the given data may be looked upon as a random sample from a normal distribution. Recall: expected values for any cell cannot be below 5; combine cells if needed.

The life of a butterfly is normally distributed with a mean of 50 days. You took a random sample of 25 such butterflies. The mean life for this sample is 47 days a standard deviation of 3 days. At α = 0.05. a. Test to see if the average life of a butterfly is different from 50 days. b. Your friend believes that the life of a butterfly is less than 50 days. Is she correct?

Biological oxygen demand (BOD) is a pollution index that is monitored in the treated effluent of paper mills. A certain paper mill has taken 31 samples over the past 3 months. The mean and standard deviation for the sample data are 3.42 and 0.728 ppm respectively. The mill would like to see if this sample indicates that the true average BOD in their treated effluent exceeds the targeted 3.00 ppm. Let ? = 0.05. A) The test statistic, (ttest), for this data set is: Note: Round your answer to the nearest hundredth.B) The p-value is: C) The statistical decision and corresponding English interpretation for this study are: Fail to reject Ha: conclude that the true BOD in treated effluent exceeds 3 ppmFail to reject Ho: we cannot conclude that the true BOD in treated effluent exceeds 3 ppm    Reject Ha: we cannot conclude that the true BOD in treated effluent exceeds 3 ppmReject Ho: conclude that the true BOD in treated effluent exceeds 3 ppm

Assume that you have been provided the following information for a sample of cars The covariance between weight and miles per gallon is equal to -4.9 pound-miles. The standard deviation of the cars' mileages is 7.75. The standard deviation of the cars' weights is 0.94. Estimate the correlation coefficient to the first decimal place.