2. Let X ~ N (2856,16) a) What is the standard deviation of x? b) Calcuate P (X>7)
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2. Let X ~ N (2856,16)
a) What is the standard deviation of x?
b) Calcuate P (X>7)
2.
Given
The data is as follows:
Let
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- The mean amount of time it takes a kidney stone to pass is 12 days and the standard deviation is 4 days. Suppose that one individual is randomly chosen. Let X = time to pass the kidney stone. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(,)b. Find the probability that a randomly selected person with a kidney stone will take longer than 9 days to pass it. c. Find the minimum number for the upper quarter of the time to pass a kidney stone. days.The population of college students using “normal shoes” is able to complete a particular racecourse in an average of 250 seconds. The standard deviation for this population is 20 seconds and the population is normally distributed. A random sample of 28 college students is given a special pair of new shoes and asked to run the course. The average “race time” for this group is 243 seconds. assume now that the designer of the shoes states that his shoes should improve the times of the user (less time to finish the race). State the hypotheses involved. determine if the hypothesis test is one tailed or two tailed Give the Z scores associated with cut-off points for .01, .05, and .10 (1%, 5%, and 10% respectively). Calculate the Z score for this problem. Based on a cut-off point or alpha level of .05 (5%), what decision would you make about your hypotheses? Explain this decision. Make conclusions regarding the specifics of this study.SAT scores in one state is normally distributed with a mean of 1532 and a standard deviation of 200. Suppose we randomly pick 50 SAT scores from that state. a) Find the probability that one of the scores in the sample is less than 1492. P(X < 1492) = b) Find the probability that the average of the scores for the sample of 50 scores is less than 1492. P(X < 1492) = Round each answer to at least 4 decimal places.
- The percent of fat calories that a person in America consumes each day is normally distributed with a mean of 36 and a standard deviation of 10. Suppose that one individual is chosen at random. Find the following (round to 4 decimal places) a) Find the probability that the percent of fat calories a person consumes is more than 40. b) Find the probability that the percent of fat calories a person consumes is less than 35. c) Find the maximum number for the lower quartile of percent of fat calories. d) The middle 70% of the percent of fat calories are from 4 toThe number of ants per acre in the forest is normally distributed with mean 42,000 and standard deviation 12,112. Let X = number of ants in a randomly selected acre of the forest. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(,)b. Find the probability that a randomly selected acre in the forest has fewer than 36,786 ants. c. Find the probability that a randomly selected acre has between 31,002 and 37,024 ants. d. Find the first quartile. ants (round your answer to a whole number)14
- The number of ants per acre in the forest is normally distributed with mean 42,000 and standard deviation 12,269. Let X = number of ants in a randomly selected acre of the forest. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(,)b. Find the probability that a randomly selected acre in the forest has fewer than 32,912 ants. c. Find the probability that a randomly selected acre has between 37,038 and 47,452 ants. d. Find the first quartile. ants (round your answer to a whole number)What is the probability of observing at least 60 cardinal birds in 2012? (Hint: Apply a continuity correction where appropriate.) The observers wish to identify a normal range for the number of cardinal birds observed per year. The normal range will be defined as the interval (L, U), where L is the largest integer ≤ 15th percentile and U is the smallest integer ≥ 85th percentile . mean= 61.71 standard deviation= 9.58 probability of at least 60 birds in 2012 is 0.5714 i was able to figure out all of this but am having trouble finding the exact interval.Suppose the mean grade for a statistic midterm was 75 with Standard Deviation of 10. Assume that the grades are normally distributed. a) What percentage of students received a grade less than 70? b) If 2 students failed the exam i.e. their grades were less than 60, how many students took the test? ( Hint: Focus on x< 60 first)
- Today, the waves are crashing onto the beach every 5.1 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 5.1 seconds. Round to 4 decimal places where possible. The mean of this distribution is The standard deviation is The probability that wave will crash onto the beach exactly 1.4 seconds after the person arrives is P(x = 1.4) = The probability that the wave will crash onto the beach between 1.3 and 4.7 seconds after the person arrives is P(1.3 < x < 4.7) = The probability that it will take longer than 3.92 seconds for the wave to crash onto the beach after the person arrives is P(x > 3.92) = Suppose that the person has already been standing at the shoreline for 1.1 seconds without a wave crashing in. Find the probability that it will take between 2.4 and 3.8 seconds for the wave to crash onto the shoreline. 84% of the time a person will wait at least how long before the wave crashes in?…SAT scores in one state is normally distributed with a mean of 1481 and a standard deviation of 88. Suppose we randomly pick 49 SAT scores from that state. a) Find the probability that one of the scores in the sample is less than 1457. P(X<1457)P(X<1457) = b) Find the probability that the average of the scores for the sample of 49 scores is less than 1457. P(¯¯¯X<1457)P(X¯<1457) =The number of ants per acre in the forest is normally distributed with a mean of 43,000 and a standard deviation of 12,222. Let X = number of ants in a randomly selected acre of the forest. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(----,----)b. Find the probability that a randomly selected acre in the forest has fewer than 57,110 ants. (------)c. Find the probability that a randomly selected acre has between 44,908 and 53,418 ants. (-------)d. Find the first quartile. (-------) ants (round your answer to a whole number)
