Question

The daily high temperature on October 31 in a certain city is normally distributed with µ = 50 and σ = 8 . What is the probability that the high temperature on October 31 in a randomly chosen year will be between 46 degrees and 58 degrees? (Give your answer as a decimal rounded to 4 decimal places.)

Answer 1

0.5328

Explanation:

µ = 50

σ = 8

We are supposed to find the probability that the high temperature on October 31 in a randomly chosen year will be between 46 degrees and 58 degrees

`P(46 < x< 58)`

Formula :
`Z=(x-\mu)/(\sigma)`

at x = 46

`Z=(46-50)/(8)`

`Z=-0.5`

Refer the z table for p value

p value = 0.3085

at x = 58

`Z=(58-50)/(8)`

`Z=1`

Refer the z table for p value

p value = 0.8413

`P(46 < x< 58)=P(x<58)-P(x<46)= 0.8413-0.3085=0.5328`

Hence the probability that the high temperature on October 31 in a randomly chosen year will be between 46 degrees and 58 degrees is 0.5328