Question

The distribution of IQ scores is a nonstandard distribution with a mean of 100 and a standard deviation of 15, and a bell-shaped graph is drawn to represent this distribution.

1. Find the area under the curve
2. Find the value of the median
3. Find the value of the mode
4. Find P (x > 120)
5. Find m for P(x < m) = 0.7257
6. Find m for P(x > m) = 0.7257
7. Find the probability that 36 random people has a mean of at least 110.

Answer 1

1) area under the curve =1 (since under any probability distribution is always 1)

2) value of the median =mean=100

3) value of the mode =100

4)

probability =P(X>120)=P(Z>(120-100)/15)=P(Z>1.33)=1-P(Z<1.33)=1-0.9082=0.0918

5)

for 72.57th percentile critical value of z=0.60

therefore corresponding value x=mean+z*std deviation=109

6)

since P(X>m) =0.7257

P(X<m) =1-0.7257 =0.2743

for 27.43th percentile critical value of z=-0.6

therefore corresponding value=mean+z*std deviation=91

7)

std error=σx̅=σ/√n=15/√36 =

2.5000

probability that 36 random people has a mean of at least 110 :

probability =P(X>110)=P(Z>(110-100)/2.5)=P(Z>4)=1-P(Z<4)=1-1=0.0000