Question

The prices of the tablets in a store have a mean of $840 and a standard deviation of $70. Use normcdf on your calculator to find the following probabilities. Express your answers as decimals rounded to three spaces. 1. P (the tablet will be less than $700) = 2.P (the tablet will be between $800 and $900) = 3.P (the tablet will be greater than $850) =

Answer 1

1)
Here, μ = 840, σ = 70 and x = 700. We need to compute P(X <= 700). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (700 - 840)/70 = -2

Therefore,
P(X <= 700) = P(z <= (700 - 840)/70)
= P(z <= -2)
= 0.0228

2)
P(800 <= X <= 900) = P((900 - 840)/70) <= z <= (900 - 840)/70)
= P(-0.57 <= z <= 0.86) = P(z <= 0.86) - P(z <= -0.57)
= 0.8051 - 0.2843
= 0.5208

3)
P(X >= 850) = P(z <= (850 - 840)/70)
= P(z >= 0.14)
= 1 - 0.5557 = 0.4443