Question

In: Statistics and Probability

1. assume that adults have IQ scores that are normally distributed with a mean of 100...

1. assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15. Find the probability that a randomly selected adult has an IQ between 105 and 125.

2. 120 142 158 128 135 152

Find x̅, s, and t, construct a 90% confidence interval pf the population mean.

Solutions

Expert Solution

Solution :

Given that,

mean = = 100

standard deviation = = 15

1 ) P (105 < x < 125 )

P (105 - 100 / 15) < ( x -  / ) < (125 - 100 /15)

P ( 5 / 15 < z 25 / 15 )

P (0.33 < z < 1.67)

P ( z < 1.67 ) - P ( z < 0.33)

Using z table

= 0.9525 - 0.6293

= 0.3232

Probability = 0.3232Solution:

x x2
120 14400
142 20164
158 24964
128 16384
135 18225
152 23104
∑x=835 ∑x2=117241


Mean ˉx=∑xn

=120+142+158+128+135+152/6

=835/6

=139.1667

Sample Standard deviation S=√∑x2-(∑x)2nn-1

=√117241-(835)26/5

=√117241-116204.1667/5

=√1036.8333/5

=√207.3667

=14.4002

Degrees of freedom = df = n - 1 = 6 - 1 = 5

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

t /2,df = t0.05,5 =2.015

Margin of error = E = t/2,df * (s /n)

= 2.015 * (14.40 / 625)

= 11.85

Margin of error = 11.85

The 90% confidence interval estimate of the population mean is,

- E <  < + E

139.17 - 11.85 < < 139.17 + 11.85

127.32 < < 151.02

(127.32, 151.02 )


Related Solutions

8. Assume that adults have IQ scores that are normally distributed with a mean of 100...
8. Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test). Let X be the IQ scores for adults. So ( ) 2 X N~ 100,15 a. Find the probability that a randomly selected adult has an IQ greater than 131.5 (the requirement for membership in the Mensa organization). Show the area under the normal curve. b. Find the probability that a randomly selected...
Assume that adults have IQ scores that are normally distributed with a mean of 105 and...
Assume that adults have IQ scores that are normally distributed with a mean of 105 and a standard deviation of 15. Find the probability that a randomly selected adult has an IQ between 92 and 118.
assume the adults have IQ scores that are normally distributed with a mean of 100.2 and...
assume the adults have IQ scores that are normally distributed with a mean of 100.2 and a standard deviation of 17.7. find the probability that a randomly selected adult has an IQ greater than 128.9. The probability that randomly selected adult from this group has an IQ greater than 128.9 is ____.
Assume that adults have IQ scores that are normally distributed with a mean of 95.9 and...
Assume that adults have IQ scores that are normally distributed with a mean of 95.9 and a standard deviation of 16.4. Find the following probabilities. Round your answers to three decimal places; add trailing zeros as needed. The probability that a randomly selected adult has an IQ greater than 122.6 is . The probability that a randomly selected adult has an IQ lower than 92.0 is . The probability that a randomly selected adult has an IQ between 80.0 and...
Assume that adults have IQ scores that are normally distributed, with a mean of 102 and...
Assume that adults have IQ scores that are normally distributed, with a mean of 102 and a standard deviation of 16. Find the probability that a randomly selected individual has an IQ between 81 and 109. Choose the correct value: Choose one: a) 0.5647 b) 0.5749 c) 0.5747 d) 0.5649
Assume that adults have IQ scores that are normally distributed with a mean of 99.1 and...
Assume that adults have IQ scores that are normally distributed with a mean of 99.1 and a standard deviation of 18.6 Find the probability that a randomly selected adult has an IQ greater than 133.0
Assume that adults have IQ scores that are normally distributed with a mean of 102.6and a...
Assume that adults have IQ scores that are normally distributed with a mean of 102.6and a standard deviation of 18.7 Find the probability that a randomly selected adult has an IQ greater than 131.5 ​(Hint: Draw a​ graph.) The probability that a randomly selected adult from this group has an IQ greater than 131.5 is ????
Assume that adults have IQ scores that are normally distributed with a mean of 97.7 and...
Assume that adults have IQ scores that are normally distributed with a mean of 97.7 and a standard deviation 21.8 Find the first quartile Upper Q1, which is the IQ score separating the bottom​ 25% from the top​ 75%. (Hint: Draw a​ graph.) The first quartile is ________. ​(Type an integer or decimal rounded to one decimal place as​ needed.)
Assume that adults have IQ scores that are normally distributed with a mean of 95.8 and...
Assume that adults have IQ scores that are normally distributed with a mean of 95.8 and a standard deviation of 22.4. Find the probability that a randomly selected adult has an IQ greater than 127.6. ​(Hint: Draw a​ graph.) The probability that a randomly selected adult from this group has an IQ greater than 127.6 is nothing. ​(Round to four decimal places as​ needed.)
Assume that adults have IQ scores that are normally distributed with a mean of mu equals...
Assume that adults have IQ scores that are normally distributed with a mean of mu equals μ=105 and a standard deviation sigma equals σ=15. Find the probability that a randomly selected adult has an IQ between 95 and 115.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT