The owner of a computer repair shop has determined that their daily revenue has mean $7200 and standard deviation $1200. The daily revenue totals for the next 30 days will be monitored. What is the probability that the mean daily revenue for the next 30 days will exceed $7000? Round to four decimal places.

0.0853

Step-by-step explanation:

Step 1

The first step would be to find the Z score

Formula for Z score is given as

z = x - μ / (σ : √n)

Where

x = observed value

μ = mean

σ = Standard deviation

n = sample size

In the question we were given the above values as:

x = observed value = $7500

μ = mean = $7200

σ = Standard deviation = $1200

n = samples size = 30

Z score (z) = $7500 - $7200 / ($1200: √30)

Z score = $300 / ($1200 : √30)

Z score = 1.3693063938

Approximately, the Z score = 1.37

Step 2

Using this formula:

1 - P (z > 1.37)

Using the Standard distribution table,

P (z > 1.37) is given as

0.9146565

Therefore,

1 - P (z > 1.37)

= 1 - 0.9146565

= 0.0853435

In the question we were asked to round it up to 4 decimal places

= 0.0853

Therefore, the probability that the mean daily revenue for the next 30 days will exceed $7000 is 0.0853.