Question

1) Assume that the salaries of elementary school teachers in the United States are normally distributed with a mean of $32,0000 and a standard deviation of $3000. If 100 teachers are randomly selected, find the probability that their mean salary is greater than $32,500.

2) A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 450 seconds and a standard deviation of 50 seconds. The fitness association wants to recognize the fastest 10$ of the boys with certificates of recognition. What time would the boys need to beat in order to earn a certificate of recognition from the fitness association?

3) The mean annual income for adult women in one city is $28,520 and the standard deviation is $6000. The distribution of incomes is skewed to the right. Find the mean and standard error of the mean for this sampling distribution when using random samples of size 78. Round your answers to the nearest dollar.

Answer 1

1) Let the salary of the teachers be denoted by random variable by X.

So, X ~ N(32000 , 3000²)

So, probability that the mean salary of 100 teachers is greater than $32500 = Probability that the salary of a teacher is greater than $32500.

P(X > $32500)

= 1 - P(X < $32500)

= 1 - P(Z < ($32500 - $30000)/$3000)

= 1 - P(Z < 0.83333)

= 1 - 0.798

= 0.202.

So, the probability that mean salary is greater than $32500 is 0.202.

Please send other questions separately.