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Assignment 4- Lecture 4

Draw the distribution curve for each question and show all steps and working.

1. (5 Points) Hereford cattle are one of the most popular breeds of beef cattle. Based on data from the Hereford Cattle Society, the mean weight of a one-year-old Hereford bull is 1245 pounds, with a standard deviation of 97 pounds. Would it be unusual for the mean weight of 120 head of cattle to be less than 1130 pounds?

2. (5 points) The length of a pregnancy from conception to birth is approximately normally distributed with mean µ = 282 days and standard deviation σ = 10 days. A pregnancy is considered full-term if it lasts between 245 days and 285 days. What proportion of pregnancies are full-term?

3. (5 points) Mensa is an organization whose membership is limited to people whose IQ is in the top 5 % of the population. Assume that scores on an IQ test are normally distributed with mean µ =200 and standard deviation σ =20. What is the minimum score needed to qualify for membership on Mensa?

4. (5 points) Based on data from the U.S. Census, the mean age of college students in 2008 was µ =20 years, with a standard deviation σ = 5.8 years. A simple random sample of 75 students is drawn. What is the probability that the sample mean age of the students is greater than 30 years?