Question

The finishing times for a long-distance race are normally distributed, with an average finishing time of 3.25 hours and a standard deviation of 0.5 hours. If Bob is running this race, what time does heed to finish in order to beat 80% of the other participants?

Full step by step on how to complete. On Ti-84 and by hand.

Answer 1

In TI84

Press 2nd -> vars -> invNorm

DISTR DRAW i normalpdf 2: normalcdf 5A invNorni 4 invTS 5: tpdf 6: tcdfc 7.1X2 pdf

Filled the required information

invnom area:.8 .: 3.25 T: 0.5 Paste

invNorm(0.8.3.2! 3.670810617

X = 3.67

P ( X < 3.67 ) = 0.80

And by hand

X ~ N ( µ = 3.25 , σ = 0.5 )
P ( X < x ) = 80% = 0.8
To find the value of x
Looking for the probability 0.8 in standard normal table to calculate critical value Z = 0.8416
Z = ( X - µ ) / σ
0.8416 = ( X - 3.25 ) / 0.5
X = 3.67
P ( X < 3.67 ) = 0.8