Math Problem Solver

Use the following scenario to answer Qs 6 - 9

As described in Example 1 on p. 118 of your statistics textbook, the average IQ score is 100 with a standard deviation of 15.

Worked example from textbook: If you select a random sample of 10 people, what is the probability that the mean IQ for this sample will be less than 95? (Use Equation 6.2 and Appendix 1 (Table A1.1) from your statistics textbook to help answer this question), (Round off to 3 decimal places)

z=(x ̅-μ)/(σ/√n)

z=(95-100)/(15/√10)

z=(-5)/(15/√10)

z = -1.054 (i.e., a z-score of 1.054)

p = 0.146 (i.e., the probability that our sample of 10 secondary school learners will have a mean IQ score less than 95 is 0.146 – or a 14.6% chance)

If you select a random sample of 10 people, what is the probability that the mean IQ for this sample will be less than 90? [3] (Use Equation 6.2 and Appendix 1 (Table A1.1) from your statistics textbook to help answer this question), (Round off to 3 decimal places)

z=(x ̅-μ)/(σ/√n)

z=(?-?)/(?/√(?))

z=?/(?/√(?))

z = ?

p = ?

If you select a random sample of 40 people, what is the probability that the mean IQ for this sample will be greater than 90? [3] (Use Equation 6.2 and Appendix 1 (Table A1.1) from your statistics textbook to help answer this question), (Round off to 3 decimal places)

z=(x ̅-μ)/(σ/√n)

z=(?-?)/(?/√(?))

z= ?/(?/√(?))

z = ?

p = ?

If you select a random sample of 30 people, what is the probability that the mean IQ of this sample will be less than 90? [3] (Use Equation 6.2 and Appendix 1 (Table A1.1) from your statistics textbook to help answer this question), (Round off z score to 3 decimal places, and p score to 4 decimal places)

z=(x ̅-μ)/(σ/√n)

z=(?-?)/(?/√(?))

z=?/(?/√(?))

z = ?

p = ?