Early on the morning of April 15 1912 the RMS Titanic collid

Early on the morning of April 15, 1912, the RMS Titanic collided with an iceberg as she made her maiden voyage from Southampton UK to New York City USA. Although this British passenger liner was designed with advanced safety features including watertight compartments with remotely activated watertight doors, she only carried enough lifeboats for 1,178 people due to outdated maritime safety regulations. The ship\'s hull plates buckled inwards along her starboard side due to the collision, flooding five of her sixteen watertight compartments. 1,514 of the 2,224 aboard perished, making this sinking one of the deadliest commercial peacetime maritime disasters

Suppose that ticket prices for first class parlor suites were normally distributed with a mean of 890 pounds and a standard deviation of 25 pounds. What is the probability (correct to three decimal places) that a random sample of 30 first class parlor suite passengers would have paid an average of more than 900 pounds for their tickets?

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    900      
u = mean =    890      
n = sample size =    30      
s = standard deviation =    25      
          
Thus,          
          
z =    2.19089023      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   2.19089023   ) =    0.014229868 or 1.423% [ANSWER]