Question

The age of Facebook users is normally distributed. The average age of a user on Facebook is 40.5 with a standard deviation of 10. 1. What is the probability that a single randomly selected person that is on Facebook is less than 20 years of​ age? (round to four​ decimals) nothing 2. What is the probability that a sample of 15 Facebook useres is between 30 and 40 years of​ age?

Answer 1

Solution :

Given that ,

mean = = 40.5

standard deviation = = 10.1

1)

P(x < 20) = P((x - ) / < (20 - 40.5) / 10.1)

= P(z < -2.0297)

P(x < 20) = 0.0212

Probability = 0.0212

2)

n = 15

= 40.5

= / n = 10.1 / 15 = 2.6078

P(30 < < 40) = P((30 - 40.5) / 2.6078 <( - ) / < (40 - 40.5) / 2.6078))

= P(-4.0264 < Z < -0.1917)

= P(Z < -0.1917) - P(Z < -4.0264)   

= 0.424 - 0

= 0.424

Probability = 0.4240