plz answer following 9 questions
plz answer following 9 questions
1. Some statistics students estimated that the amount of change daytime statistics students carry is exponentially distributed with a mean of $0.72. Suppose that we randomly pick 25 daytime statistics students.
In words, define the random variable X.
Give the distribution of X.
In words, define the random variable X-.
Give the distribution of X. (Round your standard deviation to three decimal places.)
Find the probability that an individual had between $0.66 and $0.93. (Round your answer to four decimal places.)
Find the probability that the average of the 25 students was between $0.66 and $0.93. (Round your answer to four decimal places.)
2. In 1940 the average size of a U.S. farm was 174 acres. Let’s say that the standard deviation was 51 acres. Suppose we randomly survey 46 farmers from 1940.
In words, define the random variable X.
In words, define the random variable X-.
Give the distribution of X-. (Round your standard deviation to two decimal places.)
The middle 50% of the distribution for X-,the bounds of which form the distance represented by the IQR, lies between what two values? (Round your answers to two decimal places.)
| acres | (smaller value) |
| acres | (larger value) |
3. Which of the following is NOT TRUE about the distribution for averages?
4. Yoonie is a personnel manager in a large corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of 1.2 hours. Let X be the random variable representing the time it takes her to complete one review. Assume X is normally distributed. Let X be the random variable representing the mean time to complete the 16 reviews. Assume that the 16 reviews represent a random set of reviews.
Complete the distributions. (Enter exact numbers as integers, fractions, or decimals.)
(a)X ~
 |
,
 |
(b)X ~
|
,
|
5. According to the Internal Revenue Service, the average length of time for an individual to complete (keep records for, learn, prepare, copy, assemble, and send) IRS Form 1040 is 10.21 hours (without any attached schedules). The distribution is unknown. Let us assume that the standard deviation is two hours. Suppose we randomly sample 36 taxpayers.
Give the distribution of X-. (Round your answers to two decimal places.)
Find the probability that the 36 taxpayers took an average of more than 12 hours to finish their Form 1040s. (Round your answer to four decimal places.)
6. Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 149 minutes with a standard deviation of 11 minutes. Consider 49 of the races.
Let X- = the average of the 49 races.
Give the distribution of X-. (Round your standard deviation to two decimal places.)
Find the probability that the runner will average between 146 and 151 minutes in these 49 marathons. (Round your answer to four decimal places.)
Find the 60th percentile for the average of these 49 marathons. (Round your answer to two decimal places.)
Find the median of the average running times.
7. The length of songs in a collector’s iTunes album collection is uniformly distributed from two to 3.6 minutes. Suppose we randomly pick five albums from the collection. There are a total of 43 songs on the five albums.
Give the distribution of X. (Enter exact numbers as integers, fractions, or decimals.)
Give the distribution of X-. (Round your answers to four decimal places.)
Find the first quartile for the average song length. (Round your answer to two decimal places.)
Find the IQR (interquartile range) for the average song length. (Round your answer to two decimal places.)
8.Salaries for teachers in a particular elementary school district are normally distributed with a mean of $43,000 and a standard deviation of $5,700. We randomly survey ten teachers from that district. (Round your answers to the nearest dollar.)
(a) Find the 90th percentile for an individual teacher’s salary.
$
(b) Find the 90th percentile for the average teacher’s salary.
$
9.A typical adult has an average IQ score of 105 with a standard deviation of 20. If 19 randomly selected adults are given an IQ test, what is the probability that the sample mean scores will be between 87 and 125 points? (Round your answer to five decimal places.)
