Question

The average annual salary for all u.s. teachers is $47,750. assume that the distribution is normal and the standard deviation is $5680. find the probability that a randomly selected teacher earns

a. between $35,000 and $45,000 a year
b. more than $40,000 a year
c. if you were applying for a teaching position and were offered $31,000 a year, how would you feel (based on this information)?

Answer 1

The question involves calculating probabilities for a teacher's salary on a normal distribution with a mean of $47,750 and a standard deviation of $5,680. The probabilities for specified salary ranges are sought using Z-scores and a standard normal distribution table.

Step-by-step explanation:

The student is asking about the probability of a U.S. teacher's salary falling within certain intervals, given that the average annual salary is $47,750 with a standard deviation of $5,680, and the distribution is normal.

• To find the probability of a teacher earning between $35,000 and $45,000, we calculate the Z-scores for both values and refer to the standard normal distribution table.
• The probability of a teacher earning more than $40,000 is found by calculating the Z-score for $40,000 and subtracting the corresponding standard normal distribution value from 1.
• If an offer is made at $31,000, based on the provided average and standard deviation, this salary is significantly below the mean and can be considered quite low.

Please note that these probabilities assume that salaries are normally distributed and do not account for external factors such as years of experience, location, education level, or type of institution.

Answer 2

between 35k and 45k
so answer a.