The mean score for freshmen on an aptitude test at a certain college is 540, with a standard deviation of 50. Assume the means to be measured to any degree of accuracy. What is the probability that two groups selected at random, consisting of 32 and 50 students, respectively, will differ in their mean scores by less than 5 points. 0.3400 O None of these (Place answer in solution paper) 0.3300 0.6700 0.6600
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- The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2967 and standard deviation 539. One randomly selected customer is observed to see how many calories X that customer consumes. Round all answers to 4 decimal places where possible.b. Find the probability that the customer consumes less than 2600 calories. c. What proportion of the customers consume over 3342 calories? d. The Piggy award will given out to the 2% of customers who consume the most calories. What is the fewest number of calories a person must consume to receive the Piggy award? calories. (Round to the nearest calorie)The number of ants per acre in the forest is normally distributed with mean 42,000 and standard deviation 12,221. Let X = number of ants in a randomly selected acre of the forest. Round all answers to 4 decimal places where possible. b. Find the probability that a randomly selected acre in the forest has fewer than 32,793 ants. c. Find the probability that a randomly selected acre has between 46,676 and 51,692 ants. d. Find the first quartile. ? ants (round your answer to a whole number) PLEASE ANSWER THE 3 SUBS B, C AND DThe Boeing 157-200 ER aircraft carries 200 passengers and has doors with a height of 72 inches. Male heights are normally distributed with a mean of 67.4 inches and a standard deviation of 3.8 inches. 1. If a male passenger is selected at random, find the probability that he can pass through the door without leaning over. Enter your answer to four decimal places. 2. If half of the 200 passengers are men, find the probability that the average height of the 100 men is less than 72 inches. Enter your answer to four decimal places.
- Assume that adults have IQ scores that are normally distributed with a mean of 97.9 and a standard deviation of 24.8. Find the probability that a randomly selected adult has an IQ greater than 135.8. The probability that a randomly selected adult from this group has an IQ greater than 135.8 is?The average amount of money spent for lunch per person in the college cafeteria is $5.99 and the standard deviation is $2.1. Suppose that 49 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible. For the group of 49 patrons, find the probability that the average lunch cost is between $5.77 and $6.08.Cody took his first physics exam and scored an 80. The population mean for this exam is 70, and the standard deviation is 5. What is the probability of selecting a person with a score greater than Cody’s?
- A random variable X forms a normally distributed data set with mean 94.2 and standard deviation 2.41 . Determine the probability that X is at most 94.2. (Express your final answer in 4 decimal places)The NJ Department of Health has reported the average life span of NJ residents is 81 years. If the standard deviation is σ = 4 years, what is the probability of a person living to at least 92 years of age?A population of values has a mean of 38.5 and standard deviation of 80.4. Find the probability that a sample of 247 values from this population will have a mean between 31.3 and 44.1.
- Assume that adults have IQ scores that are normally distributed with a mean of95.4 and a standard deviation of 16.6. Find the probability that a randomly selected adult has an IQ greater than 118.1 The probability that a randomly selected adult from this group has an IQ greater than 118.1 is what?From a sample with n = 12, the mean number of televisions per household is 2 with a standard deviation of 1 television. Using Chebychev's Theorem, determine at least how many of the households have between 0 and 4 televisions. At least of the households have between 0 and 4 televisions. (Simplify your answer.)The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 67 minutes and a standard deviation of 16 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.b. Find the probability that a randomly selected person at the hot springs stays longer then 77 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 (IQR) for time spent at the hot springs.Q1: (. ) minutesQ3: ( )minutesIQR:( )minutes PLEASE ANSWER ALL 3 SUBS B, C, AND D