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Standard normal curve, car towing calls, new curriculum

Please provide step by step solution.

Instructions: Solve the following problems keep the guidelines below in check.
If you are calculating something using a table, the number of decimal places from the table is expected. like z=1.00, table value is .8413 (2 decimal places for z, 4 for the probability)

REGARDING NUMBER OF DECIMAL PLACES:
IF AN ANSWER CALLS FOR 4 DECIMAL PLACES (FOR EXAMPLE), CALCULATE TO 5 DECIMAL PLACES AND ROUND TO 4.

7. Test scores are Normally Distributed with a mean of 65 and a Standard Deviation of 8.
Calculate the z-score of a test score of 84

8. Solve the problem: Find the area under the standard normal curve to the right of z = -1.25

9. Solve the problem: A car towing service company averages two calls per hour. Use the Poisson distribution to determine the probability that in a randomly selected hour the number of calls is six.

10. 0.32 of all college students like the idea of a new curriculum.
If we select 88 students (ASSUME INDEPENDENCE), what is the Standard Deviation of the Probability Distribution that would list the number of students (from 0 to 88) and the probability of each.
If the answer cannot be calculated, enter zero (0) as your answer.
Round to 4 decimal places otherwise. YES, you need, therefore, to look at the 5th decimal place.0.32 of all college students like the idea of a new curriculum.
If we select 88 students (ASSUME INDEPENDENCE), what is the Standard Deviation of the Probability Distribution that would list the number of students (from 0 to 88) and the probability of each.
If the answer cannot be calculated, enter zero (0) as your answer.
Round to 4 decimal places otherwise. YES, you need, therefore, to look at the 5th decimal place.

Solution Preview

Please see the attached files.

7. Let X denotes the test scores. Given X follows normal distribution with mean 65 and standard deviation 8.
Symbolically this can be expressed as
Standardizing
The Z score corresponding to X = 84 is = 2.38

8. Area under standard normal curve to the right of z = -1.25 is:
= 0.1056
NB. can be calculated by using the excel function NORMSDIST(-1.25)

9. Let X denotes the number of calls per hour. X can be approximated by Poisson distribution with λ = 2
Probability that in a ...

Solution Summary

Standard normal curve, car towing calls, and new curriculum are examined.

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