Question

Use the normalcdf feature on the calculator to find the specified area under the standard normal distribution curve. Round your answers to four decimal places (to the nearest ten-thousandth).

To the left of z = 2.05

Find the probability below for the normal distribution with mean μ = 12.5 and standard deviation σ = 1.6. Give your answer as a percent rounded to the nearest hundredth (two decimal places).

P(12.8 < X < 13.1)

Answer 1

Solution :

Given that,  

Using standard normal table ,

P(z < 2.05) = 0.9798

mean = = 12.5

standard deviation = = 1.6

P(12.8 < x < 13.1) = P[(12.8 - 12.5)/ 1.6) < (x - ) /  < (13.1 - 12.5) / 1.6) ]

= P(0.1875 < z < 0.375)

= P(z < 0.375) - P(z < 0.1875)

= 0.6462 - 0.5744

= 0.0718

P(12.8 < x < 13.1) = 7.18%