6.20 z-score for given probability in tails For a normal TRY distribution, a. Find the z-score for which a total probability of 0.02 falls more than z standard deviations (in either direction) from the mean, that is, below p Zo or above + zo. b. For this z, explain why the probability more than z standard deviations above the mean equals 0.01. c. Explain why +2.330 is the 99th percentile.
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- Los Angeles workers have an average commute of 30 minutes. Suppose the LA commute time is normally distributed with a standard deviation of 13 minutes. Let X represent the commute time for a randomly selected LA worker. a. What is the distribution of X? X - N( b. Find the probability that a randomly selected LA worker has a commute that is longer than 27 minutes. Round to 4 decimal places. c. Find the 70th percentile for the commute time of LA workers. Round to 2 decimal places. minutesThe number of ants per acre in the forest is normally distributed with mean 44,000 and standard deviation 12,192. 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( 44,000 12,192 b. Find the probability that a randomly selected acre in the forest has fewer than 47,638 ants. c. Find the probability that a randomly selected acre has between 45,935 and 56,143 ants. d. Find the first quartile. ants (round your answer to a whole number)Los Angeles workers have an average commute of 30 minutes. Suppose the LA commute time is normally distributed with a standard deviation of 15 minutes. Let X represent the commute time for a randomly selected LA worker. 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 LA worker has a commute that is longer than 34 minutes. c. Find the 85th percentile for the commute time of LA workers. minutes
- Los Angeles workers have an average commute of 31 minutes. Suppose the LA commute time is normally distributed with a standard deviation of 13 minutes. Let X represent the commute time for a randomly selected LA worker. Round all answers to 4 decimal places where possible.a. Find the probability that a randomly selected LA worker has a commute that is longer than 27 minutes. b. Find the 70th percentile for the commute time of LA workers. minutesThe percent of fat calories that a person consumes each day is normally distributed with a mean of about 35 and a standard deviation of about ten. Suppose that 9 individuals are randomly chosen. Let X = average percent of fat calories. For the group of 9, find the probability that the average percent of fat calories consumed is more than six. (Round your answer to four decimal places.)The age of children in kindergarten on the first day of school is uniformly distributed between 4.88 and 5.8 years old. A first time kindergarten child is selected at random. Round answers to 4 decimal places if possible. a. The mean of this distribution is b. The standard deviation is c. The probability that the the child will be older than 5 years old? d. The probability that the child will be between 5.38 and 5.58 years old is e. If such a child is at the 40th percentile, how old is that child? years old.
- The age of children in kindergarten on the first day of school is uniformly distributed between 4.91 and 5.97 years old. A first time kindergarten child is selected at random. Round answers to 4 decimal places if possible. a. The mean of this distribution is b. The standard deviation is c. The probability that the the child will be older than 5 years old?The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 74 minutes and a standard deviation of 17 minutes. Suppose one person at the hot springs is randomly chosen. Let X - the amount of time that person spent at Grover Hot Springs. 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 at the hot springs stays longer then 85 minutes. c. The park service is considering offering a discount for the 4% of their patrons who spend the least time at the hot springs. What is the longest amount of time a patron can spend at the hot springs and still receive the discount? minutes. d. Find the Inter Quartile Range (1QR) for time spent at the hot springs. Q1: minutes Q3: minutes IQR: minutesThe age of children in kindergarten on the first day of school is uniformly distributed between 4.77 and 5.95 years old. A first time kindergarten child is selected at random. Round answers to 4 decimal places if possible. a. The mean of this distribution is b. The standard deviation is c. The probability that the the child will be older than 5 years old? d. The probability that the child will be between 5.27 and 5.67 years old is e. If such a child is at the 35th percentile, how old is that child? years old. Question Help: D Video 1 D Video 2 Written Example 1 Message instructor Submit Question Jump to Answer M DEL
- The average American man consumes 9.5 grams of sodium each day. Suppose that the sodium consumption of American men is normally distributed with a standard deviation of 0.8 grams. Suppose an American man is randomly chosen. Let X = the amount of sodium consumed. Round all numeric answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. Find the probability that this American man consumes between 9.2 and 10.1 grams of sodium per day. c. The middle 20% of American men consume between what two weights of sodium? Low: High:The age of children in kindergarten on the first day of school is uniformly distributed between 5 and 5.74 years old. A first time kindergarten child is selected at random. Round answers to 4 decimal places if possible. a. The mean of this distribution is 5.37 b. The standard deviation is 0.2136 c. What is the probability that the child will be older than 5.4 years old? 0.4595 d. The probability that the child will be between 5.4 and 5.6 years old is e. If such a child is at the 77th percentile, how old is that child? years old.Los Angeles workers have an average commute of 29 minutes. Suppose the LA commute time is normally distributed with a standard deviation of 12 minutes. Let X represent the commute time for a randomly selected LA worker. a. What is the distribution of X? X - N( b. Find the probability that a randomly selected LA worker has a commute that is longer than 37 minutes. Round to 4 decimal places. c. Find the 70th percentile for the commute time of LA workers. Round to 2 decimal places. minutes