Question

A population of values has a normal distribution with mean=155.9 and standard deviation=42.1. You intend to draw a random sample of size=12. Find the probability that a single randomly selected value is less than 172.9. P(X<172.9). Find the probability that a sample of size=12 is randomly selected with a mean less than 172.9. P(M<172.9). Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer 1

Solution :

Given that,

mean = = 155.9

standard deviation = = 42.1

A ) P(X < 172.9)

P ( X - /) < (172.9 - 155.9 /42.1)

P( z < 17 / 42.1 )

P ( z < 0.40 )   

Using z table

= 0.6554

Probability = 0.6554

B ) n = 12

= 155.9

₌ / n = 42.1 12 = 12.1532

P(M < 172.9)

P ( M - /) < (172.9 - 155.9 /12.1532)

P( z < 17 / 12.1532 )

P ( z < 1.399 )   

Using z table

= 0.9191

Probability = 0.9191