Question

The average teacher's salary in X-city is $37,230. Assume a normally distribution with standard deviation of the population of $5,100. For a sample of 75 teachers, what is the probability that the sample mean is less than $38,000? 0.1245 0.0934 0.4782 0.9066

Answer 1

Solution :

Given that ,

mean = = 37230

standard deviation = = 5100

n = 75

= 37230 and

= / n = 5100 / 75 = 588.8973

P( < 38000) = P(( - ) / < (38000 - 37230) / 588.8973)

= P(z < 1.32)

Using standard normal table,

P( < 38000) = 0.9066

Probability = 0.9066