If the average daily income of a person is is Php 400 with a standard deviation of Php 50, what is the probability that a man found at random has an income of at least Php 500 per day? (A) none of the choices B) 0.0168 C) 0.9772 D 0.0228
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- what is the probability that the average length of hands is less than 187 for a group of 18 men. The mean is 188 and the standard deviation is 7.1 using the central limit theoremThe mean age for a person getting married for the first time is 26.1 years. Assume the ages for first marriages are normal with a standard deviation of 4.7 years. (Give probability answers to four decimal places.) a) What is the probability that a person being married for the first time is between 21.3 and 29.2 years old? b) What is the probability that a person being married for the first time is over 28.6 years old? c) What is the probability that a person being married for the first time is between 26.5 and 33.2 years old? d) 90% of people getting married for the first time do so before what age?The mean cholesterol levels of women age 45-59 in Ghana, Nigeria, and Seychelles is 5.1 mmol/l and the standard deviation is 1.0 mmol/l. AsSume that cholesterol levels are normally distributed and a random sample of 21 women are selected. It is possible with rounding for a probability to be 0.0000.
- Suppose that a category of world-class runners are known to run a marathon (26 miles) in an average of 147 minutes with a standard deviation of 11 minutes. Consider 49 of the races. Let x̅ = the average of the 49 races. A) Give the distribution x̅ (round your standard deviation to two decimal places.) x̅~______(______,______) B) Find the probability that the average of the sample will be between 144 and 148 minutes in these 49 marathons. (Round your answer to four decimal places.) C) Find the 70th percentile for the average of these 49 marathons. (Round your answer to two decimal places.) ______ min D) Find the median of the average running times. _____minThe population mean time it takes to empty a bottle of liquid is 80 minutes with a standard deviation of 6 minutes. A sample of 60 bottles is taken. What is the probability that the sample mean is at most 78 minutes? A) 0.9951 B 0.9963 C) 0.0037 D) 0.004922
- A statistics final exam produces scores that are approximately normally distributed with a mean of 225 points and a standard deviation of 20 points. There are 300 points possible on the exam, and scores are always whole numbers. Find the probability that a student scores a) 270 points or higher on this exam.b) 180 points or lower on this exam c) Between 210 points and 255 points on this exam, inclusive.d) No higher than 240 points on this exam.The mean score for a test was 81 .52 with a standard deviation of 9.2. The scores are normally distributed. If a person is selected at random find that the probability that his/her score was: (Round to the nearest 1 000 th ) Less than 75 Between 5 and 9 More than 95a) What is the probability that a randomly selected adult in the U.S. has at least one grandparent who was born outside of the U.S.? b) find the expected number of grandparents who were born outside of the U.S. that a randomly selected adult in this country has. (Find the mean of X) c) find the standard deviation of X. Round to 4 decimal places.
- Suppose that a random variable Z is distributed according to the normal distribution, with mean 6 and standard deviation 4. What is the probability that Z takes on a value between -1 and 3? Based on the previous concept, code a snippet in RStudio and show the respective graphic of the probability.D = 129 , E = 56 , F = 134