Suppose that a histogram of a data set is approximately symmetric and

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. 
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. 
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. 

A popular retail store knows that the purchase amounts by its customers is a random variable that follows a normal distribution with a mean of $30 and a standard deviation of $9. 

What are the two dollar amounts, equidistant from the mean of $30, such that 98% of all customer purchases are between these values? Place your answers in the blanks provided. Do not include a dollar sign. For example, 14.25 would be a legitimate entry. 

Lower value   
Upper value   

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. 
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. 
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. 

Suppose that the average weekly earnings for employees in general automotive repair shops is $450, and that the standard deviation for the weekly earnings for such employees is $50. A sample of 100 such employees is selected at random. 

Find the probability that the mean of the sample is between $445 and $455. Place your answer, rounded to 4 decimal places, in the blank. For example, 0.2345 would be a legitimate entry.   

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. 
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. 
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. 

Suppose that the average weekly earnings for employees in general automotive repair shops is $450, and that the standard deviation for the weekly earnings for such employees is $50. A sample of 100 such employees is selected at random. 

Find the mean of the sampling distribution of the means of average weekly earnings for samples of size 100. Place your answer in the blank. Do not include a dollar sign. For example, 123 would be a legitimate entry.  

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. 
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. 
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. 

A popular retail store knows that the purchase amounts by its customers is a random variable that follows a normal distribution with a mean of $30 and a standard deviation of $9. 

What is the probability that a randomly selected customer will spend less than $15 at this store? Place your answer, rounded to 4 decimal places, in the blank. For example, 0.3456 would be a legitimate entry.  

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. 
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. 
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. 

A set of final exam scores in an organic chemistry course was found to be normally distributed, with a mean of 73 and a standard deviation of 8. 

What is the probability of getting a score of 68 or less on this exam? Place your answer, rounded to 4 decimal places in the blank. For example, 0.3456 would be a legitimate entry.   

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. 
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. 
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. 

Suppose that the average weekly earnings for employees in general automotive repair shops is $450, and that the standard deviation for the weekly earnings for such employees is $50. A sample of 100 such employees is selected at random. 

Find probability that the mean of the sample is less than $445. Place your answer, rounded to 4 decimal places, in the blank. For example, 0.2345 would be a legitimate entry.