Question

There is a large supply of light bulbs with the average life of 1000 hours and the standard deviation of 50 hours.

1. A light bulb is drawn at random. Find the probability that it will last more than 1020 hours.
2. A random sample of 25 light bulbs is drawn. Find the probability that the sample average life is more than 1020 hours.

Using Ti-34 calculator

Equations/answer written out using

binomcdf(x,x,x)

Binompdf(x,x,x)

Invnorm

InvT

tcdf

If possible/needed to solve the equation

Answer 1

Solution:-

a) When a light bulb is drawn at random, the probability that it will last more than 1020 hours is 0.3446.

x = 1020

By applying normal distribution:-

z = 0.40

Use the z-score table or p-value calculator.

P(z > 0.40) = 0.3446

normalcdf(1020, 10⁹⁹, 1000,50) = 0.3446

b) When a random sample of 25 light bulbs is drawn. The probability that the sample average life is more than 1020 hours is 0.0228.

x = 1020

By applying normal distribution:-

z = 2.0

Use the z-score table or p-value calculator.

P(z > 2.0) = 0.0228

normalcdf(1020, 10⁹⁹, 1000,10) = 0.0228