Some governments have set a safety limit for cadmium in dry vegetables at 0.5 part per million (ppm). Researchers measured the cadmium levels in a random sample of a certain type of edible mushroom. The accompanying table shows thedata obtained by the researchers. Find and interpret a 90% confidence interval for the mean cadmium level of all mushrooms of this type. Assume a population standard deviation of cadmium levels in mushrooms of this type of 0.27 ppm.(Note: The sum of the data is 6.72 ppm.)Click here to view the data.Click here to view page 1 of the table of areas under the standard normal curve.Click here to view page 2 of the table of areas under the standard normal curve.Mushroom cadmium levels.....ppm toThe 90% confidence interval is fromppm.(Round to three decimal places as needed.)0.3199 00.680.200.821.170.940.220.370.3509'00.40PrintDoneHelp me solve thisView an exampleGet more helpClear allCheck answer3,760AONtv23,M00MacBook AirF3000DDF7F4F5F8F10F11F12%242.3.9.7.08.6deleteR.P.205

Answered: Image /qna-images/answer/13f6cd93-351c-4319-b11f-a34117b7ce0c.jpgConsider that µ is the population mean cadmium level of all mushrooms of this type. The sum of the data is 6.72 ppm and the sample size is n = 12. The sample mean is, x̅ = 6.72/12 = 0.56, the population standard deviation is σ = 0.27 and the sample size is n = 12. The confidence level is 90%. The level of significance is α = 1 – 0.90 = 0.10. Hence, α/2 = 0.05. If 90% of the observations must lie within an interval, the remaining 10% must lie outside the interval. Further, due to symmetry, 5% will lie above the upper limit and the remaining 5% will lie below the lower limit of the interval. Thus, the upper limit of the interval is such that, 95% lie below it. As a result, from a standard normal table corresponding to row of 1.6 and column of .04, it is obtained that zα/2 = z0.05 ≈ 1.64 [Using Excel formula: =NORM.S.INV(0.95)]. Thus, the confidence interval is, The 90% confidence interval form 0.432 ppm to 0.688 ppm. It can be said with 90% confidence that, the population mean cadmium level of all mushrooms of this type lies between 0.432 ppm and 0.688 ppm.