Answer:
68.6433≤x≤82.3568
Step-by-step explanation
confidence interval formula is expressed as
CI = xbar ± z × S/√n
xbar is the mean
z is the z score at 90% = 1.645
s is the Standard deviation
N is the sample size = 5
xbar = 60+75+80+70+ 90/5
xbar = 375/5
xbar = 75
Get standard deviation
SD =√\sum(x-xbar)²/N
SD = √(60-75)²+(75-75)²+(80-75)²+(70-75)²+(90-75)²/5
SD = √15²+0²+5²+5²+15²/5
SD = √225+50+225/5
SD = √500/5
SD =√100
SD = 10
Substitute the derived values into the formula
CI = 75±1.645 × 10/√5
CI = 75 ± (1.645×4.4721)
CI = 75±7.3568
CI = (75-7.3568, 75+7.3568)
CI = (67.6433, 82.3568)
Hence the 90% confidence interval of the student is:
68.6433≤x≤82.3568