Question

The personnel office at a large electronics firm regularly schedules job interviews and maintains records of the interviews. From the past records, they have found that the length of a first interview is normally distributed, with mean μ = 34 minutes and standard deviation σ = 6 minutes. (Round your answers to four decimal places.)

(a) What is the probability that a first interview will last 40 minutes or longer?

(b) Six first interviews are usually scheduled per day. What is the probability that the average length of time for the six interviews will be 40 minutes or longer?

How hot is the air in the top (crown) of a hot air balloon? Information from Ballooning: The Complete Guide to Riding the Winds, by Wirth and Young (Random House), claims that the air in the crown should be an average of 100°C for a balloon to be in a state of equilibrium. However, the temperature does not need to be exactly 100°C. What is a reasonable and safe range of temperatures? This range may vary with the size and (decorative) shape of the balloon. All balloons have a temperature gauge in the crown. Suppose that 60 readings (for a balloon in equilibrium) gave a mean temperature of x = 97°C. For this balloon, σ ≈ 14°C.

(c) Compute a 95% confidence interval for the average temperature at which this balloon will be in a steady-state equilibrium. (Round your answers to one decimal place.)

lower limit
upper limit

Answer 1

(a)

The z-score for X =40 is

The  probability that a first interview will last 40 minutes or longer is

(b)

The z-score for is

So  the probability that the average length of time for the six interviews will be 40 minutes or longer

(c)

Answer:

Lower limit: 93.4

Upper limit: 100.6