Can you tell me if my answers true,and How can i obtain the confidence interval?

a)A samle of 10 students scored the following grades:

40,42,35,54,57,54,46,42,54,57

(i)Find the sample mean ,mode and median.

Sample mean:

Sample mode:

mode is the most frequently ocurring value:

grades frequency

40 0

42 2

35 0

54 3

57 2

46 0

In this example we have more than one modal (multimodal)

Mode=42,54,57

Median:

First we must arrange the numbers in increasing order.

35,40,42,42,46,54,54,54,57,57

Here the batch size is even,so we have 2 middle values:

First middle value occure at the position(n/2)=(10/2=5)

The first middle value is 46

secondmiddlevalue occure at the position[(n/2) +1]=6

The second middle value is 54

Median =[(46+54)/2]=50

(ii)Compute the sample standard deviation

(iii)Find 90%and 95%confidence intervals for the scores

How can I get the confidence interval ..

Here the sample size is <25 (sample size=10)

I know how to obtain the confidence interval when the sample size >25

buthow to obtain the confidence interval when the sample size <25

(B)Suppose that the grades in a course are normally distributed with mean69 and standard deviation 12.

(i)Determine the ranges in which 90%,95%,and 99% of grades lie.

Approximately 90%grades were between:

(µ -1.64 *σ) and (µ+1.64 *σ)

(69-1.64*12) and(69+1.64*12)

(69-19.68) and (69+19.68)

49.32 and 88.68

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Approximately 95%grades were between:

(µ -1.96*σ) and (µ+1.96*σ)

(69-1.96*12) and(69+1.96*12)

(69-23.52) and(69+23.52)

45.48 and 92.52

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Approximately 95%grades were between:

(µ -2.58*σ) and (µ+2.58*σ)

(69-2.58*12) and(69+2.58*12)

(69-30.96) and(69+30.96)

38.04 and 99.96

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(ii)Write down the mean and the standard error of the mean of samples of size 144.

Since n>25

x=µ=69

(iii)Find a range of values within which the means of approximately 95% of sample of size 144 lie.