Assume a variable is normally distributed with a mean of 30 and standard deviation of 6. P(x>32) = Round to three decimal places. N
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- The lengths of pregnancies in a small rural village are normally distributed with a mean of 267 days and a standard deviation of 14 days. A distribution of values is normal with a mean of 267 and a standard deviation of 14. What percentage of pregnancies last fewer than 274 days? P(X < 274 days) Let XX represent the full height of certain species of tree. Assume that XX is normally distributed with a mean of 82.1 feet and a standard deviation of 47.9 feet.Find the probability that the full height of a randomly selected tree is greater than 154 feet. P(X>154)cor A company that makes cola drinks states that the mean caffeine content per 12-ounce bottle of cola is 55 milligrams. You want to test this claim. During your tests, you find that a random sample of thirty 12-ounce bottles of cola has a mean caffeine content of 57.4 milligrams. Assume the population is normally distributed and the population standard deviation is 7.3 milligrams. At a = 0.04, can you reject the company's claim? Complete parts (a) through (e). (a) Identify Ho and H. Choose the correct answer below. OB H: u#57.4 H µ= 57.4 O A. Ho: µ = 57.4 H3: µ#57.4 C. Ho: H= 55 H: µ# 55 D. H,: u2 55 H µ<55 OF H: µz57.4 H: u< 57.4 O E. Ho: u#55 H: u= 55 (b) Find the critical value(s). Select the correct choice below and fill in the answer box within your choice. (Round to two decimal places as needed.) O A. The critical values are + O B. The critical value isA distribution of values is normal with a mean of 120 and a standard deviation of 6. Find the interval containing the mid-44% of the values. Please show your answer to 1 decimal place. Interval = ( , )
- The one in the yellow is the previous tab.Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 236 feet and a standard deviation of 44 feet. We randomly sample 49 fly balls. Part (a) If X =average distance in feet for 49 fly balls, then give the distribution of X. Round your standard deviation to two decimal places. X ____, ________,_______ ~ . Part (b) What is the probability that the 49 balls traveled an average of less than 226 feet? (Round your answer to four decimal places.)Sketch the graph. Scale the horizontal axis for X. Shade the region corresponding to the probability. Part (c) Find the 70th percentile of the distribution of the average of 49 fly balls. (Round your answer to two decimal places.) ft †A normal distribution with a mean of 2mm and a standard deviation of 0.05mm a randomly generated number of 0.71 , need to calculate the standardised Z value, from my notes Z = (actual value - mean)/standard deviation. do i take the randomly generated number of 0.81 as the actual value ?
- Scores on a history test have an average of = 70 with standard deviation of 5. What is the z-score for a student who earned a 65 on the test? What is the coefficient of variation? 2. The annual salaries of employees in a large company are approximately normally distributed with a mean of $70,000 and a standard deviation of $30,000. (6 points) What percent of people earn less than $40,000? What percent of people earn more than $85,000? What percent of people earn between $40,000 and $85,000? 3. Assume women’s heights follow a normal distribution with a mean of u = 64.5 inches and a standard deviation of 2.5 inches. Find the probability that a sample of 14 women have a mean height greater than 65 inches.A distribution of values is normal with a mean of 60 and a standard deviation of 3. Find the interval containing the mid-68% of the values. Please show your answer to 1 decimal place. Interval = (,)Assume that the mean height of men in the United States is 70 inches, with a standard deviation of 3 inches. A particular man is 80 inches tall. Find the z-score of his height. (Round to two decimal places.)
- The table below shows the summary statistics of the sales ($) made by company ABC in 2022. No. of month 12 134,562 135,000 48,997 95,000 185,000 90,000 Mean Median S.D Minimum Maximum Range The monthly profit should be adjusted by multiplying 0.88 then subtracting $30,000. Without calculating the profit for each month, find the new standard deviation of profit for 2022? (2 d.p.)Now use the binomial formulas below to find the mean and standard deviation when n = 5 and p = 0.04. Mean = u = n x p Standard Deviation = q = _/npqSuppose the average life of kiwi phones is 4.66 years with standard deviation 1.05 years. Let X represent the average lif of 40 r/s kiwi phones. Find P( x > 5)
